23.3.20 problem 9(a)

Internal problem ID [4161]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 9(a)
Date solved : Tuesday, March 04, 2025 at 05:54:35 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 13

ode:=diff(diff(y(x),x),x)-3*diff(y(x),x)+2*y(x) = 0; 
ic:=y(0) = 0, D(y)(0) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y \left (x \right ) = -{\mathrm e}^{x}+{\mathrm e}^{2 x} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 14

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

\[ y(x)\to e^x \left (e^x-1\right ) \]

✓ Sympy. Time used: 0.149 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (e^{x} - 1\right ) e^{x} \]