78.2.14 problem 5.d

Internal problem ID [20966]
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.d
Date solved : Thursday, October 02, 2025 at 07:00:46 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

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

\[ y = {\mathrm e}^{-6 x} c_1 +\frac {3 \left (x +\frac {7 c_2}{3}\right ) {\mathrm e}^{x}}{7} \]

✓ Mathematica. Time used: 0.028 (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 c_1 e^{-6 x}+e^x \left (\frac {3 x}{7}-\frac {3}{49}+c_2\right ) \end{align*}

✓ Sympy. Time used: 0.128 (sec). Leaf size: 19

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)
 

\[ y{\left (x \right )} = C_{2} e^{- 6 x} + \left (C_{1} + \frac {3 x}{7}\right ) e^{x} \]