Internal problem ID [11611]
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`]]
\[ \boxed {y \sec \left (x \right )^{2}+\left (\tan \left (x \right )+2 y\right ) y^{\prime }=-\sec \left (x \right ) \tan \left (x \right )} \]
✓ 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: 1.831 (sec). Leaf size: 101
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 {2} \sqrt {\sec ^2(x)} \sqrt {-8 \cos (x)+(-1+4 c_1) \cos (2 x)+1+4 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*}