73.17.20 problem 20

Internal problem ID [15483]
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 : 20
Date solved : Monday, March 31, 2025 at 01:39:09 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }-30 y&=0 \end{align*}

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

ode:=diff(diff(y(x),x),x)+diff(y(x),x)-30*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 \,{\mathrm e}^{11 x}+c_2 \right ) {\mathrm e}^{-6 x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 22

ode=D[y[x],{x,2}]+D[y[x],x]-30*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 e^{-6 x}+c_2 e^{5 x} \]

✓ Sympy. Time used: 0.131 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-30*y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 6 x} + C_{2} e^{5 x} \]