Internal problem ID [1711]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.10. Page 80
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-t \sqrt {1-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 12
dsolve(diff(y(t),t)=t*sqrt(1-y(t)^2),y(t), singsol=all)
\[ y \relax (t ) = \sin \left (\frac {t^{2}}{2}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 2.887 (sec). Leaf size: 78
DSolve[y'[t]==t*Sqrt[1-y[t]^2],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to -\frac {\tan \left (\frac {t^2}{2}+c_1\right )}{\sqrt {\sec ^2\left (\frac {t^2}{2}+c_1\right )}} \\ y(t)\to \frac {\tan \left (\frac {t^2}{2}+c_1\right )}{\sqrt {\sec ^2\left (\frac {t^2}{2}+c_1\right )}} \\ y(t)\to -1 \\ y(t)\to 1 \\ \end{align*}