Trying to check my work:
Solve the DE: dy/dx +4xy = x/y^2

Question

Trying to check my work:
Solve the DE: dy/dx +4xy = x/y^2

anonymous · Answer

$$y \prime + 4xy = x/y^2$$ let z = y^3 => z'/3 = (y^2)*y'$$1/3 z \prime +3xy = x$$ $$1/3(z \prime +xz)=x$$

anonymous · Answer

$$z \prime +xz = 3x$$ $$let \ u (x)= e ^{∫xdx}$$

anonymous · Answer

$$z \prime +xz = 3x$$ $$let \ u (x)= e ^{∫xdx}$$

anonymous · Answer

$$u(x) = e ^{x ^{2}/2}$$

anonymous · Answer

$$z \prime e ^{x ^{2}/2}+xye ^{x ^{2}/2}=3xe ^{x ^{2}/2}$$$$(e ^{x ^{2}/2}z)\prime=3xe ^{x ^{2}/2}$$$$e ^{x ^{2}/2}z = ∫3xe ^{x ^{2}/2}dx$$ $$e ^{x ^{2}/2}z = 3e ^{x ^{2}/2} + C$$ $$z  = 3+C \div e ^{x ^{2}/2}$$

anonymous · Answer

$$y^3 = 3+C \div e ^{x ^{2}/2}$$ $$y=\sqrt[3]{C \div e ^{x ^{2}/2}}$$

anonymous · Answer

$$
y' = x/y^2-4xy 
$$$$
y' = x(1/y^2-4y) 
$$It looks separable, though.

anonymous · Answer

ahh i see it now, $$dy/(1/y^2 - 4y) = xdx$$