85.60.1 problem 3 (b)

Internal problem ID [22852]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 203
Problem number : 3 (b)
Date solved : Thursday, October 02, 2025 at 09:15:46 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 26

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

\[ y = -\frac {x \,{\mathrm e}^{x}}{2}+c_1 \,{\mathrm e}^{x}+c_2 \,{\mathrm e}^{-x}+c_3 \,{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to c_1 e^{-x}+e^x \left (-\frac {x}{2}-\frac {1}{4}+c_2\right )+c_3 e^{2 x} \end{align*}

✓ Sympy. Time used: 0.154 (sec). Leaf size: 22

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

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