N = (2xy x 2 − 2) For a differential equation to be an exact differential equation, we need condition M y = N x M y = 2 (x y) N x = 2y 2x = 2 (x y) So, the given equation is an exact differential equation We are looking for the solution of the form Ψ (x, y) = C dΨ = Ψ x dx Ψ y dy = 0 ⇒Ψ x = (x y) 2 and Ψ y = (2xy x 2Equation is exact, so we can find F(x,y) such that Fx = M, Fy = N F(x,y) = ∫ M(x,y) dx F(x,y) = ∫ (x y)² dx F(x,y) = ∫ (x² 2xy y²) dx F(x,y) = 1/3 x³ x²y xy² g(y) F(x,y) = ∫ N(x,y) dy F(x,y) = ∫ (2xy x² − 3) dy F(x,y) = xy² x²y − 3y h(x) Comparing both values we see that h(x) =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
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Solution for 2 (2xy x)dy – x² y² y 1dx = 0 Whenx = 1;Free PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystepFind the particular solution of the differential equation (1 – y^2) (1 log x) dx 2xy dy = 0, given that y = 0 when x = 1 CBSE CBSE (Commerce) Class 12 Question Papers 1799 Textbook Solutions MCQ Online Tests 29 Important Solutions 3664 Question Bank Solutions
If 3x^22xyy2=2 then the value of dy/dx x = 1 is A 2 B 0 C 2 D 4 E not defined algebra The following identity can be used to find Pythagorean triples, where the expressions x2−y2, 2xy, and x2y2 represent the lengths of three sides of a right triangle; Explanation dy dx = 1 2xy ∴ dy dx −2xy = 1 1 This is a First Order Linear nonhomogeneous Ordinary Differential Equation of the form;=0 when =1 (1 x2) 2xy = 1 1 2 divide both sides by (1 2) 2 1 2 = 1 1 2 (1 2) 2 1 2 y = 1 1 2 comparing with py = q p = 2 1 2 & q = 1 1 2 2 find integrating
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Solution for (A) (xy)* dx(2xy x² –1)dy = 0, y(1) =1 close Start your trial now!(y^22xy)dx=(x^22xy)dy Get the answers you need, now!The given Equation is an exact differential equation Solution is given by ∫ M d x ∫ ( T e r m s i n N n o t c o n t a i n i n g x) d y = c y=constant ∫ ( 1 y − 2 x) d x ∫ 3 y d y = c x y − 2 log x 3 log y = c ADD COMMENT EDIT Please log in to add an answer
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解：∵(3x^2y2xyy^3)dx(x^2y^2)dy=0 ==>(3x^2ydx2xydxx^2dy)(y^3dxy^2dy)=0 ==>(3x^2ye^(3x)dx2xye^(3x)dxx^2e^(3x)dy)(y^3e^(3x)dxy^2e^(3x)dy)=0 (等式两端同乘e^(3x)) ==>d(x^2ye^(3x))d(y^3e^(3x))/3=0 ==>x^2ye^(3x)y^3e^(3x)/3=C/3 (C是积分常数)The differential equation 2xydy=x 2y 21dx determines A A family of circles with centre on xaxis B A family of circles with centre on yaxis C A family of rectangular hyperbiola with centre on xaxis D A family of rectangulat hyperbola with centre on yIntegrating Factors Some equations that are not exact may be multiplied by some factor, a function u (x, y), to make them exact When this function u (x, y) exists it is called an integrating factor It will make valid the following expression ∂ (u·N (x, y)) ∂x
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Solution Verified by Toppr Correct option is B) dxdy= 2xyy 2−x 2 Substitute y=vx ∴vx dxdv= 2vv 2−1⇒x dxdv=− 2v1v 2⇒ 1v 22v dv xdx=0 Integrating log(1v 2)logx=logk ∴x(1v 2)=k Substitute v= xy ⇒x 2y 2=kx Video Explanation Solve any question of Differential Equations with Patterns of problems > Was this answer helpful?Share It On Facebook Twitter Email 1 Answer 2 votes answered by rubby (525k points) selected by Vikash Kumar Best answer Integrating both sides, we get ex 96, 14 for each of the differential equations given in exercises 13 to 15 , find a particular solution satisfy the given condition 1 2 2 = 1 1 2 ;
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2xydx (y23x2)dy=0 Geometric figure Two Straight Lines Slope = 1 xintercept = 0/1 = yintercept = 0/1 = Slope = 00/00 = This is my attempt \\frac{dy}{dx} = \\frac{y^2 1}{x^2 1} \\\\ \\int \\frac{dy}{y^2 1} = \\int \\frac{dx}{x^2 1} \\\\ \\ln \\left \\frac{y1}{y1} \\rightThe functions f, g and h satisfy the relations f (x) = g(x 1) Then f " (2x) is equal to Answer 9 If x = sin − 1(3t − 4t3) and y = cos − 1(√1 − t2), then dy dx is equal to Answer 10 If y2 = 100tan − 1x 45sec − 1x, then dy dx = Answer 11 If y = sin − 1√1 − x, then dy dx is equal to Answer 12
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Join this channel to get access to perkshttps//wwwyoutubecom/channel/UCFhqELShDKKPv0JRCDQgFoQ/joinHere is the technique to solve this question and how toFirst week only $499!See the answer Solve the given initialvalue problem ( x y) 2dx (2 xy x2 − 6) dy = 0, y (1) = 1 Expert Answer 92% (26 ratings) Previous question Next question
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See answers (1) asked x ˙ = r x − h x 2 q, where x ˙ = d x d t I'm assuming r, h, q have different units I first tried τ = t t 0 and A = x x 0 Then I got d A x 0 d τ t 0 = r A x 0 − h A 2 x 0 2 qWhat is the solution of (xy^2) dx 2xy dy = 0?Separate the variables ydy = x^2 / (x 1)dx Divide x^2 by x 1 to get
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JEE Main 19 The solution of the differential equation , (dy/dx) = (xy)2 , when y(1) = 1, is (A) loge (2y/2x) = 2 (y1) (B) loge (2x/2y) =Ravinenavath869 ravinenavath869 Math Secondary School (y^22xy)dx=(x^22xy)dy 1 See answer ravinenavath869 is waiting for your help Add your answer and earn pointsCalculus Find dy/dx x^2y^2=2xy x2 y2 = 2xy x 2 y 2 = 2 x y Differentiate both sides of the equation d dx (x2 y2) = d dx (2xy) d d x ( x 2 y 2) = d d x ( 2 x y) Differentiate the left side of the equation Tap for more steps Differentiate Tap for more steps
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Dy dx P (x)y = Q(x) This is a standard form of a Differential Equation that can be solved by using an Integrating Factor I (X^22xyy^2)dx(xy^2)dy=0 1 See answer ssirissiri97 is waiting for your help Add your answer and earn pointsThis helps us sort answers on the page Absolutely not Definitely yes
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How do you solve linear firstorder differential equations? Transcript Ex 95, 4 show that the given differential equation is homogeneous and solve each of them ( ^2 ^2 ) 2 =0 Step 1 Find / ( ^2 ^2 ) 2 =0 2xy dy = ( ^2 ^2 ) dx 2xy dy = ( ^2 ^2 ) dx / = ( ^2 ^2)/2 Step 2 Putting F(x, y) = / and finding Solution Given equation is (2xyytany)dx (x 2 xtan 2 ysec 2 y)dy=0 Step 1 Comparing with Mdx Ndy = 0 M= 2xyytany and N = x 2 xtan 2 y Step 2 Check ∂M/∂y = ∂N/∂x ∂M/∂y = 2x1sec 2 y = 2xtan 2 y ∂N/∂x = 2xtan 2 y Therefore ∂M/∂y = ∂N/∂x Step 3 The general solution of equation 1 is
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyX and y are positive integers; y = (xlnx)/(1lnx) We have dy/dx = (x^2y^2xy)/x^2 with y(1)=0 Which is a First Order Nonlinear Ordinary Differential Equation Let us attempt a substitution of the form y = vx Differentiating wrt x and applying the product rule, we get dy/dx = v x(dv)/dx Substituting into the initial ODE we get v x(dv)/dx = (x^2(vx)^2x(vx))/x^2
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2 Answers { x 2 − y 2 = r 2 cos ( 2 θ) 2 x y = r 2 sin ( 2 θ) d x = cos ( θ) d r − r sin ( θ) d θ d y = sin ( θ) d r r cos ( θ) d θ When you report in the ODE, you can cancel the factor r 2, also collecting d r and d θ you'll find addition formulas for angle ( 2 θ − θ) and you will eventually getFind the particular solution of the differential equation dy/dx=(xy)/(x^2y^2) given that y = 1, when x = 0 CBSE CBSE (Commerce) Class 12 Question Papers 1799 Textbook Solutions MCQ Online `⇒−x^2/(2y^2)lny=C` Given y = 1 when x = 0 ⇒ C = 0 Thus, the particular solution of the given differential equation is given by `lnyGet an answer for 'solve the differential equation (2xy3y^2)dx(2xyx^2)dy=0 ' and find homework help for other Math questions at eNotes
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Free PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystepWe have differential equation of the form M (x,y) dx N (x,y) dy = 0 Equation is exact if ∂M/∂y = ∂N/∂x M (x,y) = xyy²y —> ∂M/∂y = x2y1 N (x,y) = x²3xy2x —→ ∂N/∂x = 2x3y2 Equation is not If y = x (mod N 1 ) and gcd(x,n) = 1, then why is itY = 0 %3D Bernoulli's or Linear Equation Solve for the particular solution of the given differential equation
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The equation y (y^21)dx x (y^2 1)dy =0 ,is directly separated as (y^2–1)dy/y (y^21) = dx/x Obtain dx/x = 2ydy/ (y^21) dy/y Integrating gives lnx = ln (y^21) iny lnC Then the solution is x (y^21)/y = K Your response is private Is this a valuable answer?Explanation Given Expression 3x 2 2xy y 2 = 2 When x = 1 then y = 1 by substituting the value of x in the above expression Differentiating on both the sides of the given expression with respect to x, we get (d / dx) (3x 2 2xy y 2) = (d / dx) (2)Calculus Examples Popular Problems Calculus Find dy/dx x^2xyy^2=1 x2 − xy y2 = 1 x 2 x y y 2 = 1 Differentiate both sides of the equation d dx (x2 −xy y2) = d dx (1) d d x ( x 2 x y y 2) = d d x ( 1) Differentiate the left side of the equation Tap for more steps
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