73.7.50 problem 50

Internal problem ID [15208]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 50
Date solved : Tuesday, January 28, 2025 at 07:49:57 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+3 y x&=6 \,{\mathrm e}^{-x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x)+3*x*y(x)=6*exp(-x^2),y(x), singsol=all)
 

\[ y = \frac {-3 \,{\mathrm e}^{-x^{2}}+c_{1}}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 21

DSolve[x^2*D[y[x],x]+3*x*y[x]==6*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-3 e^{-x^2}+c_1}{x^3} \]