8.18 problem 223

Internal problem ID [2971]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 8
Problem number: 223.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime }-{\mathrm e}^{x} \left (x +1\right )^{n +1}-n y=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 14

dsolve((1+x)*diff(y(x),x) = exp(x)*(1+x)^(n+1)+n*y(x),y(x), singsol=all)
 

\[ y \relax (x ) = \left ({\mathrm e}^{x}+c_{1}\right ) \left (x +1\right )^{n} \]

Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 17

DSolve[(1+x) y'[x]==Exp[x](1+x)^(n+1)+n y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \left (e^x+c_1\right ) (x+1)^n \\ \end{align*}