2.1851   ODE No. 1851

\[ y'(x)^3 \left (f'(x) y'(x)+f(x) y''(x)\right )-y''(x) \left (f''(x) y'(x)+2 f'(x) y''(x)+f(x) y^{(3)}(x)\right )+y'(x) \left (f^{(3)}(x) y'(x)+3 f''(x) y''(x)+3 y^{(3)}(x) f'(x)+f(x) y^{(4)}(x)\right )+\cos (y(x)) \left (q(x) y''(x)-q'(x) y'(x)\right )+2 q(x) y'(x)^2 \sin (y(x))=0 \]

✗ Mathematica : cpu = 0.739664 (sec), leaf count = 0

DSolve[2*q[x]*Sin[y[x]]*Derivative[1][y][x]^2 + Derivative[1][y][x]^3*(Derivative[1][f][x]*Derivative[1][y][x] + f[x]*Derivative[2][y][x]) + Cos[y[x]]*(-(Derivative[1][q][x]*Derivative[1][y][x]) + q[x]*Derivative[2][y][x]) - Derivative[2][y][x]*(Derivative[1][y][x]*Derivative[2][f][x] + 2*Derivative[1][f][x]*Derivative[2][y][x] + f[x]*Derivative[3][y][x]) + Derivative[1][y][x]*(3*Derivative[2][f][x]*Derivative[2][y][x] + Derivative[1][y][x]*Derivative[3][f][x] + 3*Derivative[1][f][x]*Derivative[3][y][x] + f[x]*Derivative[4][y][x]) == 0,y[x],x]
 

, could not solve

DSolve[2*q[x]*Sin[y[x]]*Derivative[1][y][x]^2 + Derivative[1][y][x]^3*(Derivative[1][f][x]*Derivative[1][y][x] + f[x]*Derivative[2][y][x]) + Cos[y[x]]*(-(Derivative[1][q][x]*Derivative[1][y][x]) + q[x]*Derivative[2][y][x]) - Derivative[2][y][x]*(Derivative[1][y][x]*Derivative[2][f][x] + 2*Derivative[1][f][x]*Derivative[2][y][x] + f[x]*Derivative[3][y][x]) + Derivative[1][y][x]*(3*Derivative[2][f][x]*Derivative[2][y][x] + Derivative[1][y][x]*Derivative[3][f][x] + 3*Derivative[1][f][x]*Derivative[3][y][x] + f[x]*Derivative[4][y][x]) == 0, y[x], x]

✗ Maple : cpu = 0. (sec), leaf count = 0

dsolve(diff(y(x),x)*(diff(diff(diff(f(x),x),x),x)*diff(y(x),x)+3*diff(diff(f(x),x),x)*diff(diff(y(x),x),x)+3*diff(f(x),x)*diff(diff(diff(y(x),x),x),x)+f(x)*diff(diff(diff(diff(y(x),x),x),x),x))-diff(diff(y(x),x),x)*f*diff(diff(diff(y(x),x),x),x)+diff(y(x),x)^3*(diff(f(x),x)*diff(y(x),x)+f(x)*diff(diff(y(x),x),x))+2*q(x)*diff(y(x),x)^2*sin(y(x))+(q(x)*diff(diff(y(x),x),x)-diff(q(x),x)*diff(y(x),x))*cos(y(x))=0,y(x))
 

, could not solve

dsolve(diff(y(x),x)*(diff(diff(diff(f(x),x),x),x)*diff(y(x),x)+3*diff(diff(f(x),x),x)*diff(diff(y(x),x),x)+3*diff(f(x),x)*diff(diff(diff(y(x),x),x),x)+f(x)*diff(diff(diff(diff(y(x),x),x),x),x))-diff(diff(y(x),x),x)*f*diff(diff(diff(y(x),x),x),x)+diff(y(x),x)^3*(diff(f(x),x)*diff(y(x),x)+f(x)*diff(diff(y(x),x),x))+2*q(x)*diff(y(x),x)^2*sin(y(x))+(q(x)*diff(diff(y(x),x),x)-diff(q(x),x)*diff(y(x),x))*cos(y(x))=0,y(x))