Internal problem ID [2109]
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 40.
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*} With initial conditions \begin {align*} [y \relax (0) = 3, y^{\prime }\relax (0) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 15
dsolve([diff(y(x),x$2)=x*exp(x),y(0) = 3, D(y)(0) = 4],y(x), singsol=all)
\[ y \relax (x ) = \left (-2+x \right ) {\mathrm e}^{x}+5 x +5 \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 18
DSolve[{y''[x]==x*Exp[x],{y[0]==3,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (x-2)+5 (x+1) \\ \end{align*}