81.14.2 problem 18-12

Internal problem ID [21687]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 18. Algebra of differential operators. Page 435
Problem number : 18-12
Date solved : Thursday, October 02, 2025 at 08:00:00 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }+5 y^{\prime }-12 y&=0 \end{align*}

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

ode:=2*diff(diff(y(x),x),x)+5*diff(y(x),x)-12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\frac {3 x}{2}}+c_2 \,{\mathrm e}^{-4 x} \]

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

ode=2*D[y[x],{x,2}]+5*D[y[x],x]-12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{3 x/2}+c_2 e^{-4 x} \end{align*}

✓ Sympy. Time used: 0.093 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-12*y(x) + 5*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 4 x} + C_{2} e^{\frac {3 x}{2}} \]