78.12.11 problem 1 (k)

Internal problem ID [18219]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 17. The Homogeneous Equation with Constant Coefficients. Problems at page 125
Problem number : 1 (k)
Date solved : Thursday, March 13, 2025 at 11:49:25 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.000 (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: 0.014 (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: 0.153 (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)
 

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