82.10.4 problem Ex. 4

Internal problem ID [18759]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 27
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:15:19 PM
CAS classification : [_linear]

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

✓ Solution by Maple

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

dsolve((x+1)*diff(y(x),x)-n*y(x)=exp(x)*(x+1)^(n+1),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: 0.077 (sec). Leaf size: 17

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

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