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
Solve The Differential Equation X 2 1 Dy Dx 2xy 1 X 2 1 Sarthaks Econnect Largest Online Education Community
