## jms_zacher Group Title dy/dx = (y^2 + 2xy)/x^2 homogeneous diff equation one year ago one year ago

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1. mukushla

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

2. jms_zacher

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

3. waleed_imtiaz

... Seperate the variables integrate them

4. mukushla

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?