Internal problem ID [2104]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.2, Basic Ideas and Terminology. page
21
Problem number: Problem 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-{\mathrm e}^{x} x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)=x*exp(x),y(x), singsol=all)
\[ y \relax (x ) = \left (-2+x \right ) {\mathrm e}^{x}+x c_{1}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 19
DSolve[y''[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (x-2)+c_2 x+c_1 \\ \end{align*}