86.5.11 problem 11

Internal problem ID [23125]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5a at page 74
Problem number : 11
Date solved : Thursday, October 02, 2025 at 09:23:07 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }+2 y^{\prime }-2 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 25

ode:=3*diff(diff(y(x),x),x)+2*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{\frac {2 x \sqrt {7}}{3}}+c_2 \right ) {\mathrm e}^{-\frac {\left (1+\sqrt {7}\right ) x}{3}} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to e^{-\frac {1}{3} \left (1+\sqrt {7}\right ) x} \left (c_2 e^{\frac {2 \sqrt {7} x}{3}}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.113 (sec). Leaf size: 29

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

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