The equation is y 2 = 3 x 2 − 2 x y The first thing I would do is get all the "y"s on the left by adding 2xy to both sides y 2 2 x y = 3 x 2 Now, instead of factoring or using the quadratic formula, I would complete the square The coefficient of y is 2x Half of that is x so we can "complete the square" on the left by adding x 2 to bothCreate your account View this answer (x23y2) dx−2xy dy = 0 ( x 2Is an example of homogeneous function OTRUE O FALSE TRUE FALSE close Start your trial now!
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X y 2 x2 2xy y2 example-Tap for more steps Multiply x 2 x 2 by x 2 x 2 by adding the exponents Tap for more steps Use the power rule a m a n = a m n a m a n = a m n to combine exponents Add 2 2 and 2 2 Rewrite using the commutative property of multiplication Multiply y 2Answer (1 of 5) Let v=y/x so that vx\dfrac{dv}{dx}=\dfrac{dy}{dx}=\dfrac{2xy}{y^2x^2} =\dfrac{2v}{v^21}\tag*{} This DE in v and x is separable, leading to x\dfrac
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X Y x=y2 y=x2 (1,1) (4,2) Figure 2 The area between x = y2 and y = x − 2 split into two subregions If we slice the region between the two curves this way, we need to consider two different regions Where x > 1, the region's lower bound is the straight line For x < 1, however, the region's lower bound is the lower half of the1) = 12 ( 1)2 8(1)( 1) = 1 1 8 = 6Copied to clipboard x^{2}2yxy^{2}=0 All equations of the form ax^{2}bxc=0 can be solved using the quadratic formula \frac{b±\sqrt{b^{2}4ac}}{2a} The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction x=\frac{2y±\sqrt{\left(2y\right)^{2}4y^{2}}}{2}
Cancel out xy in both numerator and denominator Cancel out − x y in both numerator and denominator Expand the expression Expand the expression Multiply \frac {y^ {2}2xyx^ {2}} {x^ {2}y^ {2}} times \frac {2x} {xy} by multiplying numeratorExtended Keyboard Examples Upload Random f(x,y)=x^2y^2 WolframAlpha Compute answers using Wolfram's breakthrough technology & knowledgebase,Answer (1 of 5) One easy technique to solve this type of math 1 From given equation need to find, dy/dx (if numerator and denominator have same degree then result will be homogenous) 2 Then let y=vx =>dy/dx=v dv/dx 3 Now from point 1 what value you got equal it to from 2
Advanced Math Q&A Library f(x,y) = x2 2xy y?2xy = 2 ⋅x⋅y 2 x y = 2 ⋅ x ⋅ y Rewrite the polynomial x2 2⋅x⋅yy2 x 2 2 ⋅ x ⋅ y y 2 Factor using the perfect square trinomial rule a2 2abb2 = (ab)2 a 2 2 a b b 2 = ( a b) 2, where a = x a = x and b = y b = y (xy)2 ( x y) 2 Let b = ( x y) So, now you have x ( b) y ( b) = x b y b = b x b y Now factor out the $\color {blue} {b}# b ( x y) Remember, b = x y, so substitute ( x y) ( x y) = ( x y) 2 Share Follow this answer to receive notifications
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v ( x, y) = 3 x 2 y y 2 − ( 4 / 3) y 3 β ( X) and after trying to solve for β I found it equal to β = x 2 y − x 2 and after applying it to the v ( x, y) = 4 x 2 y 2 = ( 4 / 3) y 3 − x 2 which in obviously is not applying CR equations if we wantJust plug x^2 2xy=0 into your first equation You get y= 1 or y=1 Then plug those two into the solutions you got for x So you get x=2 or x=0 or x=2Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!
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HInt 2x^2x(2y)y^22y2=0 As x is real, the discriminant must be \ge0 (2y)^28(y^22y2)\ge0\iff0\ge4(y2)^2\iff(y2)^2\le0 But as y is real, (y2)^2\ge0 The equation of circle passing through (0,0) and points of intersection of the circle x^2 y^2 2x 4y 4 = 0 and yExtended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, musicProblem 2 Determine the global max and min of the function f(x;y) = x2 2x2y2 2y2xy over the compact region 1 x 1;
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For example, they can help you get started on an exercise, or they can allow you to check whether your intermediate results are correct Try to make less use of the full solutions as you work your way ∂y = 2xy Integrate i) u = xy 2−x φ(y) , φ is arbitrary functionWe can try to factor x 2 −2xy−y 2 but we must do some rearranging first Change signs y 2 2xy−x 2 = − 1 k 2 Replace − 1 k 2 by c y 2 2xy−x 2 = cHere are some basic examples 1 If z = f(x,y) = x4y3 8x2y y4 5x, then the partial derivatives are ∂z ∂x = 4x3y3 16xy 5 (Note y fixed, x independent variable, z dependent variable) ∂z ∂y = 3x4y2 8x2 4y3 (Note x fixed, y independent variable, z dependent variable) 2 If z = f(x,y) = (x2 y3)10 ln(x), then the partial
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Related » Graph » Number Line » Examples 2xy^24=2(3x^2y)y' en Related Symbolab blog posts Advanced Math Solutions – Ordinary Differential Equations Calculator, Separable ODE Last post, we talked about linear first order differential equations In this post, weAnswer and Explanation 1 Given that b2−2x2 =2xyy2 b 2 − 2 x 2 = 2 x y y 2 Let us determine the locus b2−2x2 = 2xyy2 b2 −2x2x2 = 2xyy2 x2 Adding x2on both sides b2−x2 = (xyA(x;y) = x2 y2 8xy and we have Q A(1;
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So − ϵ δ ≤ 2 δ − y 2 δ − x 2 ≤ ϵ δ Now I need to square all the sides ϵ 2 δ 2 ≤ 2 ( δ − y 2) ( δ − x 2) ≤ ϵ 2 δ 2 If this is a valid move, then 2 δ 2 − 2 δ x 2 2 x 2 y 2 − 2 δ y 2 = ϵ 2 δ 2 Solving for δ gives me δ = − x 2 − y 2 ± x 4 2 x 2 y 2 ϵ 2Answer (1 of 5) x/y=3/2 divide equation by y2 x2y2/x2y2=(x/y)21/(x/y)21 put value of x/y in equation =(3/2)21/(3/2)21 =13/5Example f X,Y (x, y) = 30 xy 2 for 0 < x < 1 and x1 < y < 1x (0 otherwise) Set up the equation to find E (XY) Expected Values of Functions of Independent RVs If X and Y are independent then E (g (X) h (Y)) = E (g (X)) E (h (Y)) Example f X,Y (x, y) = 6 xy 2 0 < x < 1, 0 < y < 1 0 OW 140
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0 y 2 Solution We look for the critical points in the interior3 For each solution ( x,y,z,,µ), find f(x,y,z) and compare the values you get The largest value corresponds to maximums, the smallest value corresponds to minimums 5 Examples Example 51 Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints xy z =0and x2 2z2 =1 f(x,y,zRelated » Graph » Number Line » Examples Factor x^{2}2xyy^{2}36 en Related Symbolab blog posts Middle School Math Solutions – Polynomials Calculator, Factoring Quadratics Just like numbers have factors (2×3=6), expressions have factors ((x2)(x3)=x^25x6) Factoring is
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Answer to Show that z = x^2 y^2 2xy satisfies Laplace's Equation By signing up, you'll get thousands of stepbystep solutions to yourRelated » Graph » Number Line » Examples \frac{\partial }{\partial x}(x^{2}2xyy^{2}) en Related Symbolab blog posts Practice, practice, practice Math can be an intimidating subject Each new topic we learn has symbols and problems we have never seen The unknowingLet p = xy and s = x y, then the equation becomes (s2 −2p−25)s 10p = (s−5)(s2 5s−2p) = 0 Hence s = 5 is an integer solution (with x = 5 and y = 0 ) Otherwise p = (s2 5s)/2 Since x,y are real Let f (xiy) = u (x,y) iv (x,y) be a holomorphic function on \Omega \subset \mathbb {C}, where u\cdot v = 1
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X^2y^2z^22xy2xz2yz Extended Keyboard Examples Upload Random Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music WolframAlpha brings expertlevelConsider the ODE {eq}(x2xye^y)dx(yx^2xe^y)dy=0{/eq} a) Show the equation is exact b) Solve the problem above with the initial condition {eq}y(1)=0{/eq}Answer and Explanation 1 Become a Studycom member to unlock this answer!
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When we have a sum (difference) of two or three numbers to power of 2 or 3 and we need to remove the brackets we use polynomial identities (short multiplication formulas) (x y) 2 = x 2 2xy y 2 (x y) 2 = x 2 2xy y 2 Example 1 If x = 10, y = 5a (10 5a) 2 = 10 2 2·10·5a (5a) 2 = 100 100a 25a 2Simplify (x^22xyy^2)/ (x/yy/x) \square!Examples Example 1 Find an implicit solution of the IVP y0= xy 2y x 2 xy 3y x 3;
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Algebra Simplify x^22xyy^2 x2 2xy y2 x 2 2 x y y 2 Nothing further can be done with this topic Please check the expression entered or try another topic x2 2xyy2 x 2 2 x y y 2Is an example of homogeneous function OTRUE O FALSE TRUE FALSE f(x,y) = x2 2xy y? $$ i^2 = j^2 = k^2 = 1 \\ ij = jk = ki = 1 $$ which sort of look like quaternions, but not quite In this case the factorisation becomes, $$ x^2 y^2 z^2 2xy 2yz 2zx = (ix jy kz)^2 $$ I didn't know if there was some algebra which obeyed these properties
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{eq}(x^2 y^2)^2 = (x^2 y^2)^2 (2xy)^2 {/eq} Identity An identity is a mathematical equality involving functions of a certain variable which is satisfied by every value of this variableDefinition and Examples Harmonic Conjugates Existence of Conjugates and ∂u ∂y = 1/x 1(y/x)2 x x2 y2 ∂2u ∂y2 −2xy (x2 y2)2 Thus ∆u = 0 and u isFree math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with stepbystep explanations, just like a math tutor
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First week only $499!In this example it is Multiply both sides by the integrating factor Simplifying we get the following** Integrate both sides Divide both sides by and we get the solution **if we take the derivative of mathe^ { /math Continue Reading This answer uses an approach involving an integrating factor rather than separation of variables Note that the integrating factor, , takes onExample Find the general solution to x2y′′ xy′ (x −2)y = 0 In standard form this ODE has p(x) = 1 x and q(x) = x −2 x2, neither of which is analytic at x = 0 However, both xp(x) = 1 and x2q(x) = x −2 are analytic at x = 0, so we have a regular singularity with p 0 = lim x→0 xp(x) = 1 and q 0 = lim x→0 x2q(x) = −2 The indicial equation is
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Derivative x^2(xy)^2 = x^2y^2 Natural Language; The factors are (xy)(xy) or (xy)^2 We need to factor the trinomial x^22xyy^2 The factors of x^2 = (x)(x) The factors of y^2 = (y)(y) Since the second sign is positive we are adding the factors meaning the signs of the factors need to be the same Since the first sign is negative both signs must be negativeGet an answer for 'solve first grade ecuation with bernoulli dy/dx = (y^22xy)/x^2 general ecuation and particular when y(1)=1' and find homework help for other Math questions at eNotes
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Answer a c x^2 (a d b c) x y b d y^2 = (a x by) (c x d y) \text{comparing this expression with} 15 x^2 2 x y 24 y^2 a c = 15\qquad a d b c = 2\qquad b d = 24 a c = 3\times 5 \text{by visual inspection} a = 3\quad c = 5\quad b = 4\quad d = 6\quad \implies 15 x^2 2 x
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