Internal problem ID [11315]
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]]
\[ \boxed {y^{\prime \prime }=x \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(diff(y(x),x$2)=x*exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (x -2\right ) {\mathrm e}^{x}+c_{1} x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 19
DSolve[y''[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (x-2)+c_2 x+c_1 \]