Internal problem ID [7847]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 267.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, _Bernoulli]
Solve \begin {gather*} \boxed {y y^{\prime } \left (\sin ^{2}\relax (x )\right )+y^{2} \cos \relax (x ) \sin \relax (x )-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 32
dsolve(y(x)*diff(y(x),x)*sin(x)^2+y(x)^2*cos(x)*sin(x)-1=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {2 x +c_{1}}}{\sin \relax (x )} \\ y \relax (x ) = -\frac {\sqrt {2 x +c_{1}}}{\sin \relax (x )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.474 (sec). Leaf size: 36
DSolve[y[x]*y'[x]*Sin[x]^2+y[x]^2*Cos[x]*Sin[x]-1==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {2 x+c_1} \csc (x) \\ y(x)\to \sqrt {2 x+c_1} \csc (x) \\ \end{align*}