12.8.2 problem 2c

Internal problem ID [1738]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.1 Homogeneous linear equations. Page 203
Problem number : 2c
Date solved : Saturday, March 29, 2025 at 11:38:10 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-2 \end{align*}

✓ Maple. Time used: 0.073 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+2*y(x) = 0; 
ic:=y(0) = 3, D(y)(0) = -2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (-5 \sin \left (x \right )+3 \cos \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

ode=D[y[x],{x,2}]-2*D[y[x],x]+2*y[x]==0; 
ic={y[0]==3,Derivative[1][y][0] ==-2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x (3 \cos (x)-5 \sin (x)) \]

✓ Sympy. Time used: 0.157 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): -2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (- 5 \sin {\left (x \right )} + 3 \cos {\left (x \right )}\right ) e^{x} \]