78.2.13 problem 5.c

Internal problem ID [20965]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 2, Second order ODEs. Problems section 2.6
Problem number : 5.c
Date solved : Thursday, October 02, 2025 at 07:00:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 6 y-5 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)-5*diff(y(x),x)+6*y(x) = 3*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x} c_2 +{\mathrm e}^{2 x} c_1 +\frac {3 \,{\mathrm e}^{x}}{2} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 29

ode=D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==3*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {3 e^x}{2}+c_1 e^{2 x}+c_2 e^{3 x} \end{align*}

✓ Sympy. Time used: 0.114 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 3*exp(x) - 5*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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