82.24.3 problem Ex. 3

Internal problem ID [18790]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 65
Problem number : Ex. 3
Date solved : Thursday, March 13, 2025 at 12:59:03 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.001 (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);
 

\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {11 x}{2}}+c_{1} \right ) {\mathrm e}^{-4 x} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 35

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

\[ y(x)\to e^{-\frac {1}{2} \left (5+\sqrt {73}\right ) x} \left (c_2 e^{\sqrt {73} x}+c_1\right ) \]

✓ Sympy. Time used: 0.158 (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)
 

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