Internal problem ID [1674]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 t}{y+t^{2} y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (2) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.049 (sec). Leaf size: 20
dsolve([diff(y(t),t) = 2*t/(y(t)+t^2*y(t)),y(2) = 3],y(t), singsol=all)
\[ y \relax (t ) = \sqrt {9-2 \ln \relax (5)+2 \ln \left (t^{2}+1\right )} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 23
DSolve[{y'[t] == 2*t/(y[t]+t^2*y[t]),y[2]==3},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sqrt {2 \log \left (t^2+1\right )+9-2 \log (5)} \\ \end{align*}