71.13.2 problem 2

Internal problem ID [14443]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number : 2
Date solved : Saturday, February 22, 2025 at 03:48:35 PM
CAS classification : [[_2nd_order, _missing_x]]

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

Using Laplace method

✓ Maple. Time used: 9.644 (sec). Leaf size: 29

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+5*y(x) = 0; 
dsolve(ode,y(x),method='laplace');
 

\[ y = \frac {{\mathrm e}^{x} \left (2 y \left (0\right ) \cos \left (2 x \right )+\sin \left (2 x \right ) \left (y^{\prime }\left (0\right )-y \left (0\right )\right )\right )}{2} \]

✓ Mathematica. Time used: 0.015 (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]
 

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

✓ Sympy. Time used: 0.142 (sec). Leaf size: 19

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

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