Internal problem ID [1673]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {t^{2} \left (1+y^{2}\right )+2 y^{\prime } y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.056 (sec). Leaf size: 16
dsolve([t^2*(1+y(t)^2)+2*y(t)*diff(y(t),t) = 0,y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \sqrt {2 \,{\mathrm e}^{-\frac {t^{3}}{3}}-1} \]
✓ Solution by Mathematica
Time used: 0.377 (sec). Leaf size: 43
DSolve[{t^2*(1+y[t]^2)+2*y[t]*y'[t] == 0,y[0]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \sqrt {2 e^{-\frac {t^3}{3}}-1} \\ y(t)\to \sqrt {2 e^{-\frac {t^3}{3}}-1} \\ \end{align*}