2.7.5 problem 5

Internal problem ID [811]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.1, second order linear equations. Page 299
Problem number : 5
Date solved : Tuesday, September 30, 2025 at 04:15:38 AM
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 )&=1 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.052 (sec). Leaf size: 15

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

\[ y = -{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 15

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

\begin{align*} y(x)&\to -e^x \left (e^x-2\right ) \end{align*}

✓ Sympy. Time used: 0.099 (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): 1, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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