50.9.11 problem 1(k)

Internal problem ID [7947]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Second-Order Linear Equations. Section 2.1. Linear Equations with Constant Coefficients. Page 62
Problem number : 1(k)
Date solved : Wednesday, March 05, 2025 at 05:19:44 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 4 y^{\prime \prime }+20 y^{\prime }+25 y&=0 \end{align*}

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

ode:=4*diff(diff(y(x),x),x)+20*diff(y(x),x)+25*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {5 x}{2}} \left (c_{2} x +c_{1} \right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 20

ode=4*D[y[x],{x,2}]+20*D[y[x],x]+25*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-5 x/2} (c_2 x+c_1) \]

✓ Sympy. Time used: 0.150 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(25*y(x) + 20*Derivative(y(x), x) + 4*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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