Internal problem ID [1677]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.4. Page 24
Problem number: 10.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\cos \left (y\right ) y^{\prime }+\frac {t \sin \left (y\right )}{t^{2}+1}=0} \] With initial conditions \begin {align*} \left [y \left (1\right ) = \frac {\pi }{2}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 35
dsolve([cos(y(t))*diff(y(t),t) = -t*sin(y(t))/(t^2+1),y(1) = 1/2*Pi],y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \arcsin \left (\frac {\sqrt {2}}{\sqrt {t^{2}+1}}\right ) \\ y \left (t \right ) &= \pi -\arcsin \left (\frac {\sqrt {2}}{\sqrt {t^{2}+1}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 16.577 (sec). Leaf size: 21
DSolve[{Cos[y[t]]*y'[t] == -t*Sin[y[t]]/(t^2+1),y[1]==Pi/2},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \arcsin \left (\frac {\sqrt {2}}{\sqrt {t^2+1}}\right ) \]