17.2.1 problem 4(a)

Internal problem ID [4118]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 4(a)
Date solved : Tuesday, September 30, 2025 at 07:05:45 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+15 y&=0 \end{align*}

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

ode:=diff(diff(y(x),x),x)+8*diff(y(x),x)+15*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{2 x}+c_1 \right ) {\mathrm e}^{-5 x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 22

ode=D[y[x],{x,2}]+8*D[y[x],x]+15*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-5 x} \left (c_2 e^{2 x}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(15*y(x) + 8*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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