3.314   ODE No. 314

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

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

Mathematica: cpu = 0.042505 (sec), leaf count = 188 $$\{\{y(x)\to -\frac{\sqrt[4]{c_1-4x^4\cos (x)+16x^3\sin (x)+48x^2\cos (x)-96x\sin (x)-96\cos (x)}}{x}\},\{y(x)\to -\frac{i\sqrt[4]{c_1-4x^4\cos (x)+16x^3\sin (x)+48x^2\cos (x)-96x\sin (x)-96\cos (x)}}{x}\},\{y(x)\to \frac{i\sqrt[4]{c_1-4x^4\cos (x)+16x^3\sin (x)+48x^2\cos (x)-96x\sin (x)-96\cos (x)}}{x}\},\{y(x)\to \frac{\sqrt[4]{c_1-4x^4\cos (x)+16x^3\sin (x)+48x^2\cos (x)-96x\sin (x)-96\cos (x)}}{x}\}\}$$

Maple: cpu = 0.047 (sec), leaf count = 170 $$\{y\left(x\right)=\frac{1}{x}\sqrt[4]{-4x^4\cos \left(x\right)+16\sin \left(x\right)x^3+48x^2\cos \left(x\right)-96\cos \left(x\right)-96x\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\frac{-i}{x}\sqrt[4]{-4x^4\cos \left(x\right)+16\sin \left(x\right)x^3+48x^2\cos \left(x\right)-96\cos \left(x\right)-96x\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\frac{i}{x}\sqrt[4]{-4x^4\cos \left(x\right)+16\sin \left(x\right)x^3+48x^2\cos \left(x\right)-96\cos \left(x\right)-96x\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=-\frac{1}{x}\sqrt[4]{-4x^4\cos \left(x\right)+16\sin \left(x\right)x^3+48x^2\cos \left(x\right)-96\cos \left(x\right)-96x\sin \left(x\right)+\mathit{\_}\mathit{C}\mathit{1}}\}$$