ODE
\[ y'(x)+4 \csc (x)=y(x)^2 \sin (x)+y(x) (3-\cot (x)) \] ODE Classification
[_Riccati]
Book solution method
Riccati ODE, Generalized ODE
Mathematica ✓
cpu = 0.327982 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \left (-4+\frac {1}{\frac {1}{5}+c_1 e^{5 x}}\right ) \csc (x)\right \}\right \}\]
Maple ✓
cpu = 0.334 (sec), leaf count = 35
\[\left [y \left (x \right ) = \frac {-4 \,{\mathrm e}^{4 x}+{\mathrm e}^{-x} \textit {\_C1}}{\sin \left (x \right ) \left ({\mathrm e}^{-x} \textit {\_C1} +{\mathrm e}^{4 x}\right )}\right ]\] Mathematica raw input
DSolve[4*Csc[x] + y'[x] == (3 - Cot[x])*y[x] + Sin[x]*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (-4 + (1/5 + E^(5*x)*C[1])^(-1))*Csc[x]}}
Maple raw input
dsolve(diff(y(x),x)+4*csc(x) = (3-cot(x))*y(x)+y(x)^2*sin(x), y(x))
Maple raw output
[y(x) = (-4*exp(4*x)+exp(-x)*_C1)/sin(x)/(exp(-x)*_C1+exp(4*x))]