87.17.13 problem 13

Internal problem ID [23605]
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 : 13
Date solved : Thursday, October 02, 2025 at 09:43:24 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&={\mathrm e}^{-2 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

ode:=diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)-4*y(x) = exp(-2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\left (-6 c_1 \,{\mathrm e}^{3 x}-6 c_3 x +x^{2}-6 c_2 \right ) {\mathrm e}^{-2 x}}{6} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 43

ode=D[y[x],{x,3}]+3*D[y[x],{x,2}]-4*y[x]==Exp[-2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{54} e^{-2 x} \left (-9 x^2+6 (-1+9 c_2) x+54 c_3 e^{3 x}-2+54 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.086 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*y(x) + 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - exp(-2*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{x} + \left (C_{1} + x \left (C_{2} - \frac {x}{6}\right )\right ) e^{- 2 x} \]