4.419   ODE No. 1419

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

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

Mathematica: cpu = 1.177650 (sec), leaf count = 53 $$\text{DSolve}[y^{″}(x)=-\frac{\sec (x)y^{\prime }(x)(x^2\sin (x)-2x\cos (x))}{x^2}-\frac{y(x)\sec (x)(2x\cos (x)-x\sin (x))}{x^2},y(x),x]$$

Maple: cpu = 0.219 (sec), leaf count = 13 $$\{y\left(x\right)=x\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}x\sin \left(x\right)\}$$