73.4.29 problem 5.4 (c)

Internal problem ID [15111]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.4 (c)
Date solved : Tuesday, January 28, 2025 at 07:31:10 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (3\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.154 (sec). Leaf size: 20

dsolve([x*diff(y(x),x)-y(x)=x^2*exp(-x^2),y(3) = 8],y(x), singsol=all)
 

\[ y = -\frac {x \left (-\frac {16}{3}+\left (\operatorname {erf}\left (3\right )-\operatorname {erf}\left (x \right )\right ) \sqrt {\pi }\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 30

DSolve[{x*D[y[x],x]-y[x]==x^2*Exp[-x^2],{y[3]==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} x \left (3 \sqrt {\pi } \text {erf}(x)-3 \sqrt {\pi } \text {erf}(3)+16\right ) \]