15.6.13 problem 13

Internal problem ID [2970]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 10, page 41
Problem number : 13
Date solved : Monday, January 27, 2025 at 07:04:53 AM
CAS classification : [_linear]

\begin{align*} \left (1+x \right ) y^{\prime }+2 y&=\frac {{\mathrm e}^{x}}{1+x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve((x+1)*diff(y(x),x)+2*y(x)=exp(x)/(1+x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x}+c_{1}}{\left (x +1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 17

DSolve[(x+1)*D[y[x],x]+2*y[x]==Exp[x]/(1+x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x+c_1}{(x+1)^2} \]