87.17.15 problem 15

Internal problem ID [23607]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 127
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:43:25 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 23

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

\[ y = -{\mathrm e}^{-x} c_1 +\frac {\left (x +2 c_2 -1\right ) {\mathrm e}^{x}}{2}+c_3 \]

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 32

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

\begin{align*} y(x)&\to e^x \left (\frac {x}{2}-\frac {3}{4}+c_1\right )-c_2 e^{-x}+c_3 \end{align*}

✓ Sympy. Time used: 0.126 (sec). Leaf size: 17

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

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