60.2.25 problem Problem 34

Internal problem ID [15205]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 34
Date solved : Thursday, October 02, 2025 at 10:07:15 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 40

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

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

✓ Mathematica. Time used: 0.245 (sec). Leaf size: 62

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

\begin{align*} y(x)&\to \frac {1}{3} e^{-x/2} \left (e^{3 x/2} (x-1+3 c_1)+3 c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+3 c_3 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 39

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

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