Question

how can salve this first order ordinary differential equation by method separation variables dy/dx=1+y+x^2+yx^2

Answer 1

Separable.

Answer 2

\[
\frac{y'}{y+1}=1+x^2
\]

Answer 3

\[
\int \frac{y'dx}{y+1}=\int 1+x^2\;dx
\]\(dy=y'dx\)\[
\int \frac{dy}{y+1}=\int 1+x^2\;dx

\]