76.13.15 problem 15

Internal problem ID [17526]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 15
Date solved : Monday, March 31, 2025 at 04:16:31 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.140 (sec). Leaf size: 14

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

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