Internal problem ID [10583]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.1 (Exact differential equations and integrating factors). Exercises page
37
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_Abel, `2nd type`, `class A`]]
\[ \boxed {y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 63
dsolve((y(x)*sec(x)^2+sec(x)*tan(x))+(tan(x)+2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -\frac {\sin \left (x \right )-\sqrt {-4 \cos \left (x \right )^{2} c_{1} +\sin \left (x \right )^{2}-4 \cos \left (x \right )}}{2 \cos \left (x \right )} \\ y \left (x \right ) = -\frac {\sin \left (x \right )+\sqrt {-4 \cos \left (x \right )^{2} c_{1} +\sin \left (x \right )^{2}-4 \cos \left (x \right )}}{2 \cos \left (x \right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.148 (sec). Leaf size: 96
DSolve[(y[x]*Sec[x]^2+Sec[x]*Tan[x])+(Tan[x]+2*y[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-2 \tan (x)-\sqrt {\sec ^2(x)} \sqrt {-16 \cos (x)+(-2+8 c_1) \cos (2 x)+2+8 c_1}\right ) \\ y(x)\to \frac {1}{4} \left (-2 \tan (x)+\sqrt {\sec ^2(x)} \sqrt {-16 \cos (x)+(-2+8 c_1) \cos (2 x)+2+8 c_1}\right ) \\ \end{align*}