50.14.5 problem 1(e)

Internal problem ID [8043]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number : 1(e)
Date solved : Wednesday, March 05, 2025 at 05:23:44 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 30

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

\[ y = {\mathrm e}^{\left (1+\sqrt {6}\right ) x} c_{2} +{\mathrm e}^{-\left (-1+\sqrt {6}\right ) x} c_{1} -\frac {x}{5}+\frac {2}{25} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 43

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

\[ y(x)\to -\frac {x}{5}+c_1 e^{x-\sqrt {6} x}+c_2 e^{\left (1+\sqrt {6}\right ) x}+\frac {2}{25} \]

✓ Sympy. Time used: 0.211 (sec). Leaf size: 32

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

\[ y{\left (x \right )} = C_{1} e^{x \left (1 - \sqrt {6}\right )} + C_{2} e^{x \left (1 + \sqrt {6}\right )} - \frac {x}{5} + \frac {2}{25} \]