64.1.2 problem 1(b)

Internal problem ID [13168]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 1(b)
Date solved : Wednesday, March 05, 2025 at 09:18:39 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-7 y^{\prime }+12 y&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-7*diff(y(x),x)+12*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{3 x} c_{1} +c_{2} {\mathrm e}^{4 x} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

ode=D[y[x],{x,2}]-7*D[y[x],x]+12*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{3 x} \left (c_2 e^x+c_1\right ) \]

✓ Sympy. Time used: 0.163 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(12*y(x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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