4.1.50 \(y'(x)=y(x) (y(x)+\sin (2 x))+\cos (2 x)\)

ODE
\[ y'(x)=y(x) (y(x)+\sin (2 x))+\cos (2 x) \] ODE Classification

[_Riccati]

Book solution method
Riccati ODE, Generalized ODE

Mathematica
cpu = 0 (sec), leaf count = 0 , crash

Kernel Crash

Maple
cpu = 0.985 (sec), leaf count = 128

\[ \left \{ y \relax (x ) =2\,{\frac {\sin \left (2\,x \right ) }{\sqrt {2\,\cos \left (2\,x \right ) +2}} \left ({\it \_C1}\, \left (\cos \left (2\,x \right ) +1 \right ) {\it HeunCPrime} \left (1,1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left (2\,x \right ) +1/2 \right ) +{\it HeunC} \left (1,1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left (2\,x \right ) +1/2 \right ) {\it \_C1}+1/2\,{\it HeunCPrime} \left (1,-1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left (2\,x \right ) +1/2 \right ) \sqrt {2\,\cos \left (2\,x \right ) +2} \right ) \left ({\it \_C1}\,{\it HeunC} \left (1,1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left (2\,x \right ) +1/2 \right ) \sqrt {2\,\cos \left (2\,x \right ) +2}+{\it HeunC} \left (1,-1/2,-1/2,-1,{\frac {7}{8}},1/2\,\cos \left (2\,x \right ) +1/2 \right ) \right ) ^{-1}} \right \} \] Mathematica raw input

DSolve[y'[x] == Cos[2*x] + y[x]*(Sin[2*x] + y[x]),y[x],x]

Mathematica raw output

""

Maple raw input

dsolve(diff(y(x),x) = cos(2*x)+(sin(2*x)+y(x))*y(x), y(x),'implicit')

Maple raw output

y(x) = 2*(_C1*(cos(2*x)+1)*HeunCPrime(1,1/2,-1/2,-1,7/8,1/2*cos(2*x)+1/2)+HeunC(
1,1/2,-1/2,-1,7/8,1/2*cos(2*x)+1/2)*_C1+1/2*HeunCPrime(1,-1/2,-1/2,-1,7/8,1/2*co
s(2*x)+1/2)*(2*cos(2*x)+2)^(1/2))*sin(2*x)/(2*cos(2*x)+2)^(1/2)/(_C1*HeunC(1,1/2
,-1/2,-1,7/8,1/2*cos(2*x)+1/2)*(2*cos(2*x)+2)^(1/2)+HeunC(1,-1/2,-1/2,-1,7/8,1/2
*cos(2*x)+1/2))