89.21.3 problem 5

Internal problem ID [24775]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Exercises at page 154
Problem number : 5
Date solved : Thursday, October 02, 2025 at 10:47:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-4 y&=15 \,{\mathrm e}^{x} \end{align*}

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

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)-4*y(x) = 15*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-4 x} c_1 +3 \left (x +\frac {c_2}{3}\right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 47

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

\begin{align*} y(x)&\to -\frac {15 e^x}{2}+c_1 e^{-\frac {1}{2} \left (1+\sqrt {17}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {17}-1\right ) x} \end{align*}

✓ Sympy. Time used: 0.111 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x \left (-1 + \sqrt {17}\right )}{2}} + C_{2} e^{- \frac {x \left (1 + \sqrt {17}\right )}{2}} - \frac {15 e^{x}}{2} \]