The solution of y,dx-(x+2y^2),dy=0 is x=f(y).

Question

The solution of $y\,dx-(x+2y^2)\,dy=0$ is $x=f(y)$. If $f(-1)=1$, then $f(a)$ [taking $a$ so that $y=1$] is:

Accepted Answer

$$\frac{y\,dx-x\,dy}{y^2}=2\,dy \implies d(x/y)=2\,dy \implies \frac{x}{y}=2y+c.$$

Using $f(-1)=1$: $c=1$. At $y=1$: $x=2+1=3$.

Solutions · 1