39.1.9 problem Problem 11.10

Internal problem ID [6514]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.10
Date solved : Wednesday, March 05, 2025 at 12:55:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y&=2 \,{\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x)-5*y(x) = 2*exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{\sqrt {5}\, x} c_2 +{\mathrm e}^{-\sqrt {5}\, x} c_1 +\frac {{\mathrm e}^{5 x}}{10} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 40

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

\[ y(x)\to \frac {e^{5 x}}{10}+c_1 e^{\sqrt {5} x}+c_2 e^{-\sqrt {5} x} \]

✓ Sympy. Time used: 0.093 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} e^{- \sqrt {5} x} + C_{2} e^{\sqrt {5} x} + \frac {e^{5 x}}{10} \]