9.15   ODE No. 1851

$$\boxed{{\displaystyle \left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)(\left(\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}f\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+3\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}f\left(x\right)\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+3\left(\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)\right)\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+f\left(x\right)\frac{{\mathrm{d}}^4}{\mathrm{d}{x}^4}y\left(x\right))-\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)f\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^3(\left(\frac{\mathrm{d}}{\mathrm{d}x}f\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+f\left(x\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right))+2q\left(x\right){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2\sin \left(y\left(x\right)\right)+(q\left(x\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-\left(\frac{\mathrm{d}}{\mathrm{d}x}q\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right))\cos \left(y\left(x\right)\right)=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.806102 (sec), leaf count = 141 $$\text{DSolve}[y^{\prime }(x{)}^3(f^{\prime }(x)y^{\prime }(x)+f(x)y^{″}(x))-y^{″}(x)(f^{″}(x)y^{\prime }(x)+2f^{\prime }(x)y^{″}(x)+f(x)y^{(3)}(x))+y^{\prime }(x)(f^{(3)}(x)y^{\prime }(x)+3f^{″}(x)y^{″}(x)+3y^{(3)}(x)f^{\prime }(x)+f(x)y^{(4)}(x))+\cos (y(x))(q(x)y^{″}(x)-q^{\prime }(x)y^{\prime }(x))+2q(x)y^{\prime }(x{)}^2\sin (y(x))=0,y(x),x]$$

Maple: cpu = 2.589 (sec), leaf count = 0 $$\text{could not solve}$$