Question

Solve
(x) dy/dx = y + 2x^2y , y(1) = e

Answer 1

This is a separable differential equation.
\[x{dy \over dx}=y(1+2x^2) \implies {dy \over y}={1+2x^2 \over x}dx.\]
Now integrate both sides.

Answer 2

Can you take it from here?

Answer 3

not really, trying to figure out

Answer 4

Let me help you with one more step
\[\int\limits {dy \over y}=\int\limits ({1 \over x}+2x)dx\]
Looks better?

Answer 5

yeah ! thanks a lot !

Answer 6

You're welcome.