76.13.6 problem 6

Internal problem ID [17517]
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 : 6
Date solved : Monday, March 31, 2025 at 04:16:17 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+6*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_1 \sin \left (\sqrt {5}\, x \right )+c_2 \cos \left (\sqrt {5}\, x \right )\right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 32

ode=D[y[x],{x,2}]-2*D[y[x],x]+6*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (c_2 \cos \left (\sqrt {5} x\right )+c_1 \sin \left (\sqrt {5} x\right )\right ) \]

✓ Sympy. Time used: 0.152 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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