Question

2. Solve Bernoulli's DE 3,,2 ах

Answer 1

Salve Bernoulli's ODE dy/dx - 1/x y = c^3 y^2 1/y^2 dy/dx -= 1/x 1/y = x^3 let v = -1/y dv/dx = + y^-2 dy/dx rightarrow 1/y^2 dy/dx = -dv/ dx pitting in gives + dv/dx + v/x = x^3 rightarrow dv/dx = x^3 where solution is v (I.F) = integral x^3. (I.f) dx +c\r\ I.F = integrating factor = e^integral 1/x dx = e^nx = x rightarrow v (x) = integral x^3. C dx + c rightarrow v. x = integral x^4 dx +c rightarrow vx = x^5/5 + c rightarrow (-1/y) x = x^5 + 5c/5 rightarrow x/y = x^2 + 5c /5 rightarrow y = -5x/x^5 + 5c