86.5.9 problem 9

Internal problem ID [23123]
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 : 9
Date solved : Thursday, October 02, 2025 at 09:23:07 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 20 y^{\prime \prime }-3 y^{\prime }-2 y&=0 \end{align*}

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

ode:=20*diff(diff(y(x),x),x)-3*diff(y(x),x)-2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {2 x}{5}}+c_2 \,{\mathrm e}^{-\frac {x}{4}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 26

ode=20*D[y[x],{x,2}]-3*D[y[x],x]-2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{2 x/5}+c_2 e^{-x/4} \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) - 3*Derivative(y(x), x) + 20*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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