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]
\[ \boxed {y^{\prime } x +y \left (2 x^{2}+1\right )=x^{3} {\mathrm e}^{-x^{2}}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve(x*diff(y(x),x) +(1+2*x^2)*y(x)=x^3*exp(-x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x^{4}+4 c_{1} \right ) {\mathrm e}^{-x^{2}}}{4 x} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 27
DSolve[x*y'[x] +(1+2*x^2)*y[x]==x^3*Exp[-x^2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x^2} \left (x^4+4 c_1\right )}{4 x} \]