Internal problem ID [1971]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-2, page 12
Problem number: 1.2-2 (e).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 y}{t +1}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 6] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve([diff(y(t),t)=2/(1+t)*y(t),y(0) = 6],y(t), singsol=all)
\[ y \relax (t ) = 6 \left (t +1\right )^{2} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 12
DSolve[{y'[t]==2/(1+t)*y[t],y[0]==6},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 6 (t+1)^2 \\ \end{align*}