Internal problem ID [8369]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Riccati]
\[ \boxed {y^{\prime }+y^{2} \sin \left (x \right )=\frac {2 \sin \left (x \right )}{\cos \left (x \right )^{2}}} \]
✓ Solution by Maple
Time used: 0.422 (sec). Leaf size: 28
dsolve(diff(y(x),x) + y(x)^2*sin(x) - 2*sin(x)/cos(x)^2=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {2 \left (\cos \left (x \right )^{3} c_{1} +1\right )}{\left (\cos \left (x \right )^{3} c_{1} -2\right ) \cos \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.926 (sec). Leaf size: 32
DSolve[y'[x] + y[x]^2*Sin[x] - 2*Sin[x]/Cos[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sec (x) \left (-2 \cos ^3(x)+c_1\right )}{\cos ^3(x)+c_1} y(x)\to \sec (x) \end{align*}