20.6.16 problem Problem 38

Internal problem ID [3711]
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 8.1, General Theory for Linear Differential Equations. page 502
Problem number : Problem 38
Date solved : Sunday, March 30, 2025 at 02:06:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=18 \,{\mathrm e}^{5 x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)+diff(y(x),x)-6*y(x) = 18*exp(5*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (3 \,{\mathrm e}^{8 x}+4 \,{\mathrm e}^{5 x} c_1 +4 c_2 \right ) {\mathrm e}^{-3 x}}{4} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 31

ode=D[y[x],{x,2}]+D[y[x],x]-6*y[x]==18*Exp[5*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {3 e^{5 x}}{4}+c_1 e^{-3 x}+c_2 e^{2 x} \]

✓ Sympy. Time used: 0.149 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - 18*exp(5*x) + Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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