29.8.18 problem 223

Internal problem ID [4823]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 8
Problem number : 223
Date solved : Monday, January 27, 2025 at 09:41:31 AM
CAS classification : [_linear]

\begin{align*} \left (1+x \right ) y^{\prime }&={\mathrm e}^{x} \left (1+x \right )^{n +1}+n y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 17

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

\[ y(x)\to \left (e^x+c_1\right ) (x+1)^n \]