\[ -f(x)+y^{(4)}(x) \sin ^6(x)+4 y^{(3)}(x) \sin ^5(x) \cos (x)-6 \sin ^6(x) y''(x)-4 \sin ^5(x) \cos (x) y'(x)+y(x) \sin ^6(x)=0 \] ✓ Mathematica : cpu = 4.95916 (sec), leaf count = 138
DSolve[-f[x] + Sin[x]^6*y[x] - 4*Cos[x]*Sin[x]^5*Derivative[1][y][x] - 6*Sin[x]^6*Derivative[2][y][x] + 4*Cos[x]*Sin[x]^5*Derivative[3][y][x] + Sin[x]^6*Derivative[4][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to x^3 \csc (x) \int _1^x\frac {1}{6} \csc ^5(K[4]) f(K[4])dK[4]+x^2 \csc (x) \int _1^x-\frac {1}{2} \csc ^5(K[3]) f(K[3]) K[3]dK[3]+x \csc (x) \int _1^x\frac {1}{2} \csc ^5(K[2]) f(K[2]) K[2]^2dK[2]+\csc (x) \int _1^x-\frac {1}{6} \csc ^5(K[1]) f(K[1]) K[1]^3dK[1]+c_4 x^3 \csc (x)+c_3 x^2 \csc (x)+c_2 x \csc (x)+c_1 \csc (x)\right \}\right \}\] ✓ Maple : cpu = 0.517 (sec), leaf count = 647
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)*sin(x)^6+4*diff(diff(diff(y(x),x),x),x)*sin(x)^5*cos(x)-6*diff(diff(y(x),x),x)*sin(x)^6-4*diff(y(x),x)*sin(x)^5*cos(x)+y(x)*sin(x)^6-f=0,y(x))
\[\text {Expression too large to display}\]