solve the following differential equation:

Question

y' + (y)tanh(x) - 2e^x = 0

Answer 1

First solve the homogeneous equation:

y' + (y)tanh(x)= 0

Replace the integration constant by an unknown function and substitute that back in the Diff. equation:

y' + (y)tanh(x) - 2e^x = 0

then solve for that unknown function.