Question

solve the differential equation (x+1) dy/dx - y = e^x(x+1)^2​

Answer 1

Answer:

The equation in normal form is dy/dx - (1/(x+1))y = (x + 1)e^x.

The integrating factor is 1/(x+1) and the solution of the equation is

y = (x+1)[ integral of ( ((x+1)e^x)(1/(x+1) )dx + C ] . Then

Yy = (x+1)( e^x + C ).