Internal problem ID [1989]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 10, page 41
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+2 y x=2 x \,{\mathrm e}^{-x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve(diff(y(x),x)+2*x*y(x)=2*x*exp(-x^2),y(x), singsol=all)
\[ y = \left (x^{2}+c_{1} \right ) {\mathrm e}^{-x^{2}} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 19
DSolve[y'[x]+2*x*y[x]==2*x*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x^2} \left (x^2+c_1\right ) \]