4.1.23 \(y'(x)=4 x \csc (x) \left (y(x)+\sin ^3(x)\right )\)

ODE
\[ y'(x)=4 x \csc (x) \left (y(x)+\sin ^3(x)\right ) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 599.993 (sec), leaf count = 0 , timed out

$Aborted

Maple
cpu = 0.71 (sec), leaf count = 114

\[ \left \{ y \relax (x ) ={{\rm e}^{-4\,i \left ({\it polylog} \left (2,{{\rm e}^{ix}} \right ) -{\it polylog} \left (2,-{{\rm e}^{ix}} \right ) \right ) }} \left (1-{{\rm e}^{ix}} \right ) ^{4\,x} \left (1+{{\rm e}^{ix}} \right ) ^{-4\,x} \left (4\,\int \!-1/2\,x \left (1-{{\rm e}^{ix}} \right ) ^{-4\,x} \left (1+{{\rm e}^{ix}} \right ) ^{4\,x}{{\rm e}^{4\,i \left ({\it polylog} \left (2,{{\rm e}^{ix}} \right ) -{\it polylog} \left (2,-{{\rm e}^{ix}} \right ) \right ) }} \left (-1+\cos \left (2\,x \right ) \right ) \,{\rm d}x+{\it \_C1} \right ) \right \} \] Mathematica raw input

DSolve[y'[x] == 4*x*Csc[x]*(Sin[x]^3 + y[x]),y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(diff(y(x),x) = 4*csc(x)*x*(sin(x)^3+y(x)), y(x),'implicit')

Maple raw output

y(x) = exp(-4*I*(polylog(2,exp(I*x))-polylog(2,-exp(I*x))))*(1-exp(I*x))^(4*x)*(
1+exp(I*x))^(-4*x)*(4*Int(-1/2*x*(1-exp(I*x))^(-4*x)*(1+exp(I*x))^(4*x)*exp(4*I*
(polylog(2,exp(I*x))-polylog(2,-exp(I*x))))*(-1+cos(2*x)),x)+_C1)