5.82   ODE No. 1530

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)\right){(\sin \left(x\right))}^2+3\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)\sin \left(x\right)\cos \left(x\right)+(\cos \left(2x\right)+4\nu (\nu +1){(\sin \left(x\right))}^2)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2\nu (\nu +1)y\left(x\right)\sin \left(2x\right)=0}}$$

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

Mathematica: cpu = 0.112514 (sec), leaf count = 58 $$\text{DSolve}[y^{\prime }(x)(4\nu (\nu +1){\sin }^2(x)+\cos (2x))+2\nu (\nu +1)y(x)\sin (2x)+y^{(3)}(x){\sin }^2(x)+3\sin (x)\cos (x)y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.187 (sec), leaf count = 113 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\left({}_2\text{F}{}_1(-\frac{\nu }{2},\frac{\nu }{2}+\frac{1}{2};\frac{1}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2})\right)}^2+\mathit{\_}\mathit{C}\mathit{2}(\cos \left(2x\right)+1){\left({}_2\text{F}{}_1(1+\frac{\nu }{2},\frac{1}{2}-\frac{\nu }{2};\frac{3}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2})\right)}^2+\mathit{\_}\mathit{C}\mathit{3}{}_2\text{F}{}_1(-\frac{\nu }{2},\frac{\nu }{2}+\frac{1}{2};\frac{1}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2})\sqrt{\cos \left(2x\right)+1}{}_2\text{F}{}_1(1+\frac{\nu }{2},\frac{1}{2}-\frac{\nu }{2};\frac{3}{2};\frac{\cos \left(2x\right)}{2}+\frac{1}{2})\}$$