Internal problem ID [4763]
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]
\[ \boxed {y^{\prime }+2 x y=x \,{\mathrm e}^{-x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)+2*x*y(x)-x*exp(-x^2)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x^{2}+2 c_{1} \right ) {\mathrm e}^{-x^{2}}}{2} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 24
DSolve[y'[x]+2*x*y[x]-x*Exp[-x^2]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-x^2} \left (x^2+2 c_1\right ) \]