The strategy to find a solution to a homogenous differential equation is to make a substitution that results in a separable equation. For a homogenous equation, either of the substitutions u Y or v =...

Extracted text: The strategy to find a solution to a homogenous differential equation is to make a substitution that results in a separable equation. For a homogenous equation, either of the substitutions u Y or v = 4. will make this y work. Let u = Y, or y = ux. Then dy = u dx + x du by the product rule. Use this substitution to simplify the given equation. xy2 dy + (-y3 + x3) dx = 0 xy2 dy – y3 dx + x³ dx = 0 их (u dx + x du) - (ux)3 dx + x3 dx 2 xy + dx + u?x4 du - (ux)3 dx + x³ dx = 0 dx + du = 0