Internal problem ID [904]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x +y \left (2 x^{2}+1\right )-x^{3} {\mathrm e}^{-x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 21
dsolve(x*diff(y(x),x) +(1+2*x^2)*y(x)=x^3*exp(-x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\frac {x^{4}}{4}+c_{1}\right ) {\mathrm e}^{-x^{2}}}{x} \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 27
DSolve[x*y'[x] +(1+2*x^2)*y[x]==x^3*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{-x^2} \left (x^4+4 c_1\right )}{4 x} \\ \end{align*}