Question

Solve for y using separation of variables
dy/dx= (1+y^2)e^x

Answer 1

Get all the terms involving x on one side, and all the terms involving y on the other:
(1/(1+ y^2)) dy = e^x dx
Integrate both sides:
arctan(y) = e^x + C
take tangent of both sides:
y = tan(e^x + C)

Answer 2

yeppers

Answer 3

Thanks!