Internal problem ID [2763]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-x \left ({\mathrm e}^{-x^{2}}+a y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(diff(y(x),x) = x*(exp(-x^2)+a*y(x)),y(x), singsol=all)
\[ y \relax (x ) = \left (-\frac {{\mathrm e}^{-\frac {x^{2} \left (2+a \right )}{2}}}{2+a}+c_{1}\right ) {\mathrm e}^{\frac {a \,x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 42
DSolve[y'[x]==x*(Exp[-x^2]+a*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{\frac {a x^2}{2}} \left (-e^{-\frac {1}{2} (a+2) x^2}+(a+2) c_1\right )}{a+2} \\ \end{align*}