85.49.4 problem 1 (d)

Internal problem ID [22805]
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 194
Problem number : 1 (d)
Date solved : Thursday, October 02, 2025 at 09:14:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 5 y+4 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x}+15 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 31

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)+5*y(x) = exp(-x)+15*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \sin \left (x \right ) c_2 +{\mathrm e}^{-2 x} \cos \left (x \right ) c_1 +\frac {{\mathrm e}^{-x}}{2}+3 x -\frac {12}{5} \]

✓ Mathematica. Time used: 0.18 (sec). Leaf size: 41

ode=D[y[x],{x,2}]+4*D[y[x],{x,1}]+5*y[x]==Exp[-x]+15*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 x+\frac {e^{-x}}{2}+c_2 e^{-2 x} \cos (x)+c_1 e^{-2 x} \sin (x)-\frac {12}{5} \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-15*x + 5*y(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)) - exp(-x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x + \left (C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )}\right ) e^{- 2 x} - \frac {12}{5} + \frac {e^{- x}}{2} \]