y′(x) = y(x)(y(x) + sin(2x)) + cos(2x)

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

${y (x) = 2 \frac{\sin (2 x)}{\sqrt{2 \cos (2 x) + 2}} (_C 1 (\cos (2 x) + 1) H e u n C P r i m e (1, 1 / 2, - 1 / 2, - 1, \frac{7}{8}, 1 / 2 \cos (2 x) + 1 / 2) + H e u n C (1, 1 / 2, - 1 / 2, - 1, \frac{7}{8}, 1 / 2 \cos (2 x) + 1 / 2)_C 1 + 1 / 2 H e u n C P r i m e (1, - 1 / 2, - 1 / 2, - 1, \frac{7}{8}, 1 / 2 \cos (2 x) + 1 / 2) \sqrt{2 \cos (2 x) + 2}) {(_C 1 H e u n C (1, 1 / 2, - 1 / 2, - 1, \frac{7}{8}, 1 / 2 \cos (2 x) + 1 / 2) \sqrt{2 \cos (2 x) + 2} + H e u n C (1, - 1 / 2, - 1 / 2, - 1, \frac{7}{8}, 1 / 2 \cos (2 x) + 1 / 2))}^{- 1}}$ 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))

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4.1.50 y′(x)=y(x)(y(x)+sin⁡(2x))+cos⁡(2x)

4.1.50 $y^{'} (x) = y (x) (y (x) + \sin (2 x)) + \cos (2 x)$