87.9.15 problem 30

Internal problem ID [23388]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 74
Problem number : 30
Date solved : Thursday, October 02, 2025 at 09:40:56 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-2*D[y[x],x]+5*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^x (c_2 \cos (2 x)+c_1 \sin (2 x)) \end{align*}

✓ Sympy. Time used: 0.053 (sec). Leaf size: 22

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

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