20.12.8 problem Problem 27

Internal problem ID [3802]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.10, Chapter review. page 575
Problem number : Problem 27
Date solved : Tuesday, March 04, 2025 at 05:16:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 27

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 29

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

\[ y(x)\to -\frac {5 e^x}{3}+c_1 e^{2 x}+c_2 e^{-2 x} \]

✓ Sympy. Time used: 0.071 (sec). Leaf size: 22

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

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