44.6.13 problem 13

Internal problem ID [7157]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 13
Date solved : Tuesday, February 04, 2025 at 12:41:03 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

\[ y = \frac {{\mathrm e}^{x}+2 c_1 \,{\mathrm e}^{-x}}{2 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.064 (sec). Leaf size: 25

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

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