Internal problem ID [10301]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 57.
Dependent variable absent. Page 132
Problem number: Ex 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x \,{\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)=x*exp(x),y(x), singsol=all)
\[ y \relax (x ) = \left (x -2\right ) {\mathrm e}^{x}+x c_{1}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.019 (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*}