85.62.1 problem 3

Internal problem ID [22863]
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 209
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:15:54 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&={\mathrm e}^{4 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)-3*y(x) = exp(4*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x} c_2 +{\mathrm e}^{-x} c_1 +\frac {{\mathrm e}^{4 x}}{5} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 31

ode=D[y[x],{x,2}]-2*D[y[x],{x,1}]-3*y[x]==Exp[4*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{4 x}}{5}+c_1 e^{-x}+c_2 e^{3 x} \end{align*}

✓ Sympy. Time used: 0.125 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x) - exp(4*x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{3 x} + \frac {e^{4 x}}{5} \]