Internal problem ID [7613]
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]
Solve \begin {gather*} \boxed {y^{\prime }+y^{2} \sin \relax (x )-\frac {2 \sin \relax (x )}{\cos \relax (x )^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 1.516 (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)
\[ y \relax (x ) = -\frac {2 \left (\left (\cos ^{3}\relax (x )\right ) c_{1}+1\right )}{\left (\left (\cos ^{3}\relax (x )\right ) c_{1}-2\right ) \cos \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.54 (sec). Leaf size: 29
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 \sec (x)-\frac {3 \cos ^2(x)}{\cos ^3(x)+c_1} \\ y(x)\to \sec (x) \\ \end{align*}