17.7.5 problem 1.2-2 (e)

Internal problem ID [3451]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-2, page 12
Problem number : 1.2-2 (e)
Date solved : Tuesday, March 04, 2025 at 04:39:39 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 y}{1+t} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6 \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 11

ode:=diff(y(t),t) = 2/(t+1)*y(t); 
ic:=y(0) = 6; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = 6 \left (t +1\right )^{2} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 12

ode=D[y[t],t]==2/(1+t)*y[t]; 
ic=y[0]==6; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 6 (t+1)^2 \]

✓ Sympy. Time used: 0.214 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Derivative(y(t), t) - 2*y(t)/(t + 1),0) 
ics = {y(0): 6} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 6 t^{2} + 12 t + 6 \]