76.13.25 problem 25

Internal problem ID [17528]
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 : 25
Date solved : Thursday, March 13, 2025 at 10:11:24 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \end{align*}

✓ Maple. Time used: 0.000 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)+diff(y(x),x)+5/4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

ode=D[y[x],{x,2}]+D[y[x],x]+125/100*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.143 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x)/4 + Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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