82.41.1 problem Ex. 1

Internal problem ID [18954]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 96
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:38:20 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

dsolve(diff(y(x),x$3)=x*exp(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (-3+x \right ) {\mathrm e}^{x}+\frac {c_{1} x^{2}}{2}+c_{2} x +c_3 \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 24

DSolve[D[y[x],{x,3}]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (x-3)+x (c_3 x+c_2)+c_1 \]