Question

Solve the differential equation (x^2)y+y'((x^2)y-x^3)=0 .. Thanks !

Answer 1

\[y'=\frac{x^2y}{x^3-x^2y}=\frac{y}{x-y}\]

now let \[z=\frac{y}{x}\] do u know where we use this method?

Answer 2

\[y'\Longrightarrow\frac{y/x}{1-y/x}\]

Answer 3

can you instruct me how did you know it's homogenous and you tried to express y' in terms of y/x ? Thanks alot !!

Answer 4

\(x^2y\) has a combined order of three

so does \(x^3\) and \(-x^2y\)

Answer 5

Thanks, i think i get it =)