I have no clue how to solve this ode , I've been watching videos, searching online, but I just can't, someone please help me.
$$2xyy' = x^2 + xy$$
2026-04-06 05:52:01.1775454721
How do I solve this specific ordinary differential equation?
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It's separable if you substitute $y=tx$ and $y'=t+xt'$ $$2y'=\frac x y+1$$ $$2(t+xt')=\frac 1 t+1$$ $$2xt'=\frac 1 t+1-2t$$ $$ 2xdt=(\frac 1 t +1 -2t)dx$$ $$ \int \frac 1 {2x}dx=\int\frac {tdt} { 1+t-2t^2}$$ $$ \frac {\ln(x)} {2}+K=\int\frac {tdt} {(1-t)(1+2t)}$$