73.17.2 problem 2

Internal problem ID [15465]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 2
Date solved : Monday, March 31, 2025 at 01:38:40 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=diff(diff(y(x),x),x)-12*diff(y(x),x)+36*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{6 x} \left (c_2 x +c_1 \right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 18

ode=D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{6 x} (c_2 x+c_1) \]

✓ Sympy. Time used: 0.146 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(36*y(x) - 12*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{6 x} \]