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]]
Solve \begin {gather*} \boxed {\sec \relax (t ) \tan \relax (t )+\left (\sec ^{2}\relax (t )\right ) y+\left (\tan \relax (t )+2 y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.027 (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 \relax (t ) = -\frac {\sin \relax (t )+\sqrt {-4 \left (\cos ^{2}\relax (t )\right ) c_{1}+\sin ^{2}\relax (t )-4 \cos \relax (t )}}{2 \cos \relax (t )} \\ y \relax (t ) = \frac {-\sin \relax (t )+\sqrt {-4 \left (\cos ^{2}\relax (t )\right ) c_{1}+\sin ^{2}\relax (t )-4 \cos \relax (t )}}{2 \cos \relax (t )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.745 (sec). Leaf size: 96
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 {\sec ^2(t)} \sqrt {-16 \cos (t)+(-2+8 c_1) \cos (2 t)+2+8 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*}