11.7.5 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, September 30, 2025 at 06:38:44 AM
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: 0.019 (sec). Leaf size: 11

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

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

✓ Mathematica. Time used: 0.017 (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]
 

\begin{align*} y(t)&\to 6 (t+1)^2 \end{align*}

✓ Sympy. Time used: 0.136 (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)
 

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