85.36.13 problem 6 (b)

Internal problem ID [22741]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 171
Problem number : 6 (b)
Date solved : Thursday, October 02, 2025 at 09:14:14 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=3 \,{\mathrm e}^{x}-2 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = 3*exp(x)-2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,{\mathrm e}^{-2 x}+c_3 \,{\mathrm e}^{3 x}-\frac {1}{3}+\frac {\left (-6 x +12 c_1 -1\right ) {\mathrm e}^{x}}{12} \]

✓ Mathematica. Time used: 0.103 (sec). Leaf size: 40

ode=D[y[x],{x,3}]-2*D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==3*Exp[x]-2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-2 x}+e^x \left (-\frac {x}{2}-\frac {1}{12}+c_2\right )+c_3 e^{3 x}-\frac {1}{3} \end{align*}

✓ Sympy. Time used: 0.194 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 3*exp(x) - 5*Derivative(y(x), x) - 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) + 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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