Question

dy/dx = (y^2 + 2xy)/x^2
homogeneous diff equation

Answer 1

well in such equations u can start with letting \[z=\frac{y}{x}\]

Answer 2

yeah i figured all of that part out. Its after integrating using partial fractions is where im stuck

Answer 3

... Seperate the variables
integrate them

Answer 4

ok so u have \[z+x\frac{dz}{dx}=\frac{z^2x^2+2zx^2}{x^2}=z^2+2z\]\[x\frac{dz}{dx}=z^2+z\]and finally\[\frac{dz}{z(z+1)}=\frac{dx}{x}\]i think this is where u were stuck so just note that\[\frac{1}{z(z+1)}=\frac{1}{z}-\frac{1}{z+1}\]makes sense?