Internal problem ID [4255]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page
403
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+2 y x -{\mathrm e}^{-x^{2}} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve(diff(y(x),x)+2*x*y(x)-x*exp(-x^2)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\frac {x^{2}}{2}+c_{1}\right ) {\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.089 (sec). Leaf size: 24
DSolve[y'[x]+2*x*y[x]-x*Exp[-x^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^{-x^2} \left (x^2+2 c_1\right ) \\ \end{align*}