Solve: $(x+1)^3y''+3(x+1)^2y'+(x+1)y=6\log(x+1)$

Is my solution correct:

Answer given in the book : $y(x+1)=c\_1+c\_2\log(x+1)+\log3(x+1)$

[![enter image description here](https://i.stack.imgur.com/xTyGt.jpg)](https://i.stack.imgur.com/xTyGt.jpg)

[![enter image description here](https://i.stack.imgur.com/SvAcz.jpg)](https://i.stack.imgur.com/SvAcz.jpg)

For my later reference: [link wolfram alpha](http://www.wolframalpha.com/input/?i=(x%20%2B%201)%5E3%20y%27%27%20%2B3(x%20%2B%201)%5E2%20y%27%20%2B%20(x%2B1)y%20%3D%206%20log(x%2B1))