3.963   ODE No. 963

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/4\frac{-4\cos \left(x\right)x+4x^2\sin \left(x\right)+4x+4+4{\left(y\left(x\right)\right)}^2+8y\left(x\right)\cos \left(x\right)x-8xy\left(x\right)+2x^2\cos \left(2x\right)+6x^2-8x^2\cos \left(x\right)+4{\left(y\left(x\right)\right)}^3+12{\left(y\left(x\right)\right)}^2\cos \left(x\right)x-12x{\left(y\left(x\right)\right)}^2+6y\left(x\right)x^2\cos \left(2x\right)+18x^{2}y\left(x\right)-24y\left(x\right)\cos \left(x\right)x^2+x^3\cos \left(3x\right)+15x^3\cos \left(x\right)-6x^3\cos \left(2x\right)-10x^3}{x}=0}}$$

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

Mathematica: cpu = 0.112014 (sec), leaf count = 108 $$\text{Solve}[-\frac{29}{3}\text{RootSum}[-29{\mathrm{\#}\text{1}}^3+3\sqrt[3]{29}\mathrm{\#}\text{1}-29\mathrm{\&},\frac{\log (\frac{\frac{3y(x)}{x}+\frac{-3x+3x\cos (x)+1}{x}}{\sqrt[3]{29}\sqrt[3]{\frac{1}{x^3}}}-\mathrm{\#}\text{1})}{\sqrt[3]{29}-29{\mathrm{\#}\text{1}}^2}\mathrm{\&}]=c_1+\frac{1}{9}{29}^{2/3}{\left(\frac{1}{x^3}\right)}^{2/3}{x}^2\log (x),y(x)]$$

Maple: cpu = 0.156 (sec), leaf count = 39 $$\{y\left(x\right)=-\cos \left(x\right)x+x-\frac{1}{3}+\frac{29\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-81{\int }^{\mathit{\_}\mathit{Z}}{(841{\mathit{\_}\mathit{a}}^3-27\mathit{\_}\mathit{a}+27)}^{-1}d\mathit{\_}\mathit{a}+\ln \left(x\right)+3\mathit{\_}\mathit{C}\mathit{1})}{9}\}$$