62.33.4 problem Ex 4

Internal problem ID [12991]
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
Date solved : Tuesday, January 28, 2025 at 04:46:29 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)=x*exp(x),y(x), singsol=all)
 

\[ y = \left (x -2\right ) {\mathrm e}^{x}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 19

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

\[ y(x)\to e^x (x-2)+c_2 x+c_1 \]