75.14.4 problem 330

Internal problem ID [16918]
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 ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 330
Date solved : Tuesday, January 28, 2025 at 09:40:52 AM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} y^{\prime \prime }&=x \,{\mathrm e}^{x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (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: 0.022 (sec). Leaf size: 15

DSolve[{D[y[x],{x,2}]==x*Exp[x],{y[0]==0,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (x-2)+x+2 \]