17.7.2 problem 1.2-2 (b)

Internal problem ID [3448]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-2, page 12
Problem number : 1.2-2 (b)
Date solved : Tuesday, March 04, 2025 at 04:39:31 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (\ln \left (3\right )\right )&=3 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 10

ode:=diff(y(t),t) = 2*y(t); 
ic:=y(ln(3)) = 3; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = \frac {{\mathrm e}^{2 t}}{3} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 14

ode=D[y[t],t]==2*y[t]; 
ic=y[Log[3]]==3; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {e^{2 t}}{3} \]

✓ Sympy. Time used: 0.116 (sec). Leaf size: 8

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

\[ y{\left (t \right )} = \frac {e^{2 t}}{3} \]