Internal problem ID [1690]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.9. Page 66
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime }=-\sec \left (t \right ) \tan \left (t \right )} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 63
dsolve(sec(t)*tan(t)+sec(t)^2*y(t)+(tan(t)+2*y(t))*diff(y(t),t) = 0,y(t), singsol=all)
\begin{align*} y \left (t \right ) = -\frac {\sin \left (t \right )+\sqrt {-4 \cos \left (t \right )^{2} c_{1} +\sin \left (t \right )^{2}-4 \cos \left (t \right )}}{2 \cos \left (t \right )} y \left (t \right ) = \frac {-\sin \left (t \right )+\sqrt {-4 \cos \left (t \right )^{2} c_{1} +\sin \left (t \right )^{2}-4 \cos \left (t \right )}}{2 \cos \left (t \right )} \end{align*}
✓ Solution by Mathematica
Time used: 1.23 (sec). Leaf size: 101
DSolve[Sec[t]*Tan[t]+Sec[t]^2*y[t]+(Tan[t]+2*y[t])*y'[t]== 0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{4} \left (-2 \tan (t)-\sqrt {2} \sqrt {\sec ^2(t)} \sqrt {-8 \cos (t)+(-1+4 c_1) \cos (2 t)+1+4 c_1}\right ) y(t)\to \frac {1}{4} \left (-2 \tan (t)+\sqrt {\sec ^2(t)} \sqrt {-16 \cos (t)+(-2+8 c_1) \cos (2 t)+2+8 c_1}\right ) \end{align*}