1its not long!!
jus think a bit..... [12]
\frac{x+y\frac{dy}{dx}}{y-x\frac{dy}{dx}}= x^2 + 2y^2 + \frac{y^{4}}{x^2}
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1hehe......ive cross multiplied and expanded and i got sum nonsense hehe........man its so long
21ho gaya!!!
hope tum logo ko atleast thoda thoda isme dikhay dega!!! its a pathetic img wid worser writing [2] \\\
aage to aaram se ho jayega simpl substiutn
1u r correct akand now take xy common in rhs...then easily variable separable form:
rhs=(xy)2(1+(y/x)2)2;
now easily variable separable
21homogenous eqtn samne dikhay pada to ywe hi meth yaad aaya.......
it mayb a tuch lenthy
but i think ans to same hi aega
1{\color{blue} \frac{x+y\frac{dy}{dx}}{y-x\frac{dy}{dx}}=x^2 + 2y^2 +\frac{y^4}{x^2} \Rightarrow \frac{xdx+ydy}{ydx-xdy}= \frac{(x^2 + y^2)^2}{x^2} \Rightarrow \frac{xdx+ydy}{\frac{ydx-xdy}{x^2}} \; \: =(x^2 + y^2)^2 \Rightarrow \frac{xdx+ydy}{(x^2 + y^2)^2}= - \frac{xdy-ydx}{x^2} }
how about this one ??