85.53.1 problem 1 (a)

Internal problem ID [22814]
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 197
Problem number : 1 (a)
Date solved : Thursday, October 02, 2025 at 09:14:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

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

\[ y = {\mathrm e}^{x} c_2 +{\mathrm e}^{-3 x} c_1 +\frac {x \,{\mathrm e}^{x}}{2} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to c_1 e^{-3 x}+e^x \left (\frac {x}{2}-\frac {1}{8}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.149 (sec). Leaf size: 17

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

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