67.11.6 problem 17.1 (f)

Internal problem ID [16607]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 17. Second order Homogeneous equations with constant coefficients. Additional exercises page 334
Problem number : 17.1 (f)
Date solved : Thursday, October 02, 2025 at 01:36:56 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }+7 y^{\prime }-6 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=3*diff(diff(y(x),x),x)+7*diff(y(x),x)-6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 24

ode=3*D[y[x],{x,2}]+7*D[y[x],x]-6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.091 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) + 7*Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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