7.1   ODE No. 1574

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

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

Mathematica: cpu = 0.206526 (sec), leaf count = 73 $$\text{DSolve}[y(x)(a^4{\sin }^4(x)-3)+y^{(4)}(x){\sin }^4(x)+2y^{(3)}(x){\sin }^3(x)\cos (x)+({\sin }^2(x)-3){\sin }^2(x)y^{″}(x)+(2{\sin }^2(x)+3)\sin (x)\cos (x)y^{\prime }(x)=0,y(x),x]$$

Maple: cpu = 0.639 (sec), leaf count = 345 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sin \left(x\right){}_2\text{F}{}_1(\frac{3}{4}+\frac{1}{4}\sqrt{-i(-4\sqrt{a+i}\sqrt{a-i}\sqrt{a-1}\sqrt{a+1}+5i)},\frac{3}{4}-\frac{1}{4}\sqrt{-i(-4\sqrt{a+i}\sqrt{a-i}\sqrt{a-1}\sqrt{a+1}+5i)};\frac{1}{2};{(\cos \left(x\right))}^2)+\mathit{\_}\mathit{C}\mathit{2}\sin \left(x\right){}_2\text{F}{}_1(\frac{3}{4}+\frac{1}{4}\sqrt{-i(4\sqrt{a+i}\sqrt{a-i}\sqrt{a-1}\sqrt{a+1}+5i)},\frac{3}{4}-\frac{1}{4}\sqrt{-i(4\sqrt{a+i}\sqrt{a-i}\sqrt{a-1}\sqrt{a+1}+5i)};\frac{1}{2};{(\cos \left(x\right))}^2)+\mathit{\_}\mathit{C}\mathit{3}\sin \left(x\right)\cos \left(x\right){}_2\text{F}{}_1(\frac{5}{4}+\frac{1}{4}\sqrt{-i(-4\sqrt{a+i}\sqrt{a-i}\sqrt{a-1}\sqrt{a+1}+5i)},\frac{5}{4}-\frac{1}{4}\sqrt{-i(-4\sqrt{a+i}\sqrt{a-i}\sqrt{a-1}\sqrt{a+1}+5i)};\frac{3}{2};{(\cos \left(x\right))}^2)+\mathit{\_}\mathit{C}\mathit{4}\sin \left(x\right)\cos \left(x\right){}_2\text{F}{}_1(\frac{5}{4}+\frac{1}{4}\sqrt{-i(4\sqrt{a+i}\sqrt{a-i}\sqrt{a-1}\sqrt{a+1}+5i)},\frac{5}{4}-\frac{1}{4}\sqrt{-i(4\sqrt{a+i}\sqrt{a-i}\sqrt{a-1}\sqrt{a+1}+5i)};\frac{3}{2};{(\cos \left(x\right))}^2)\}$$