What is the solution of dy/dx = (1+y^2)*e^x?

We have to solve dy/dx =
(1+y^2)*e^x

First we will group all the terms containing y
with dy on one side and those containing x with dx on the
other.

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

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

=> dy / (1+ y^2) - e^x dx
=0

now integrate both the side, we
get

arc tan y – e^x = C

or in
terms of y

=> arc tan y = e^x +
C

=> y = tan (e^x +
C)

Therefore the result is y = tan (e^x +
C)