Internal problem ID [1675]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sqrt {t^{2}+1}\, y^{\prime }-\frac {t y^{3}}{\sqrt {t^{2}+1}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.042 (sec). Leaf size: 16
dsolve([(t^2+1)^(1/2)*diff(y(t),t) = t*y(t)^3/(t^2+1)^(1/2),y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \frac {1}{\sqrt {1-\ln \left (t^{2}+1\right )}} \]
✓ Solution by Mathematica
Time used: 0.211 (sec). Leaf size: 19
DSolve[{(t^2+1)^(1/2)*y'[t] == t*y[t]^3/(t^2+1)^(1/2),y[0]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{\sqrt {1-\log \left (t^2+1\right )}} \\ \end{align*}