Internal problem ID [13375]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x -y=x^{2} {\mathrm e}^{-x^{2}}} \] With initial conditions \begin {align*} [y \left (3\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 20
dsolve([x*diff(y(x),x)-y(x)=x^2*exp(-x^2),y(3) = 8],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (-\frac {16}{3}+\left (\operatorname {erf}\left (3\right )-\operatorname {erf}\left (x \right )\right ) \sqrt {\pi }\right ) x}{2} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 30
DSolve[{x*y'[x]-y[x]==x^2*Exp[-x^2],{y[3]==8}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} x \left (3 \sqrt {\pi } \text {erf}(x)-3 \sqrt {\pi } \text {erf}(3)+16\right ) \]