82.41.1 problem Ex. 1

Internal problem ID [18883]
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 : Monday, March 31, 2025 at 06:18:11 PM
CAS classification : [[_3rd_order, _quadrature]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(y(x),x),x),x) = x*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x -3\right ) {\mathrm e}^{x}+\frac {c_1 \,x^{2}}{2}+c_2 x +c_3 \]

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

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

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

✓ Sympy. Time used: 0.082 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x^{2} + x \left (C_{3} + e^{x}\right ) - 3 e^{x} \]