12.2.24 problem 24

Internal problem ID [1560]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 24
Date solved : Monday, January 27, 2025 at 05:00:08 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+3 y x&={\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(x^2*diff(y(x),x) +3*x*y(x)=exp(x),y(x), singsol=all)
 

\[ y = \frac {\left (x -1\right ) {\mathrm e}^{x}+c_1}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 19

DSolve[x^2*D[y[x],x] +3*x*y[x]==Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x (x-1)+c_1}{x^3} \]