Internal problem ID [15188]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of
depression of their order. Exercises page 107
Problem number: 330.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime }={\mathrm e}^{x} x} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([diff(y(x),x$2)=x*exp(x),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y = \left (x -2\right ) {\mathrm e}^{x}+x +2 \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 15
DSolve[{y''[x]==x*Exp[x],{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (x-2)+x+2 \]