85.59.7 problem 7

Internal problem ID [22848]
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 203
Problem number : 7
Date solved : Thursday, October 02, 2025 at 09:15:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 24

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

\[ y = \frac {{\mathrm e}^{-3 x}}{10}-2 \,{\mathrm e}^{-x} c_1 +{\mathrm e}^{-\frac {x}{2}} c_2 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 33

ode=2*D[y[x],{x,2}]+3*D[y[x],{x,1}]+y[x]==Exp[-3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{-3 x}}{10}+c_1 e^{-x/2}+c_2 e^{-x} \end{align*}

✓ Sympy. Time used: 0.153 (sec). Leaf size: 22

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

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{- \frac {x}{2}} + \frac {e^{- 3 x}}{10} \]