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jms_zacher
 3 years ago
dy/dx = (y^2 + 2xy)/x^2
homogeneous diff equation
jms_zacher
 3 years ago
dy/dx = (y^2 + 2xy)/x^2 homogeneous diff equation

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mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0well in such equations u can start with letting \[z=\frac{y}{x}\]

jms_zacher
 3 years ago
Best ResponseYou've already chosen the best response.0yeah i figured all of that part out. Its after integrating using partial fractions is where im stuck

waleed_imtiaz
 3 years ago
Best ResponseYou've already chosen the best response.0... Seperate the variables integrate them

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.0ok 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?
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