3.233   ODE No. 233

$$\boxed{{\displaystyle xy\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-{\left(y\left(x\right)\right)}^2+a{x}^3\cos \left(x\right)=0}}$$

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

Mathematica: cpu = 0.024503 (sec), leaf count = 38 $$\{\{y(x)\to -x\sqrt{c_1-2a\sin (x)}\},\{y(x)\to x\sqrt{c_1-2a\sin (x)}\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 30 $$\{y\left(x\right)=\sqrt{-2a\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}}x,y\left(x\right)=-\sqrt{-2a\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}}x\}$$