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 : Monday, January 27, 2025 at 07:37:09 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

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

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