2.1574   ODE No. 1574

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

$$y(x)(a^4{\sin }^4(x)-3)+y^{(4)}(x){\sin }^4(x)+2y^{(3)}(x){\sin }^3(x)\cos (x)+({\sin }^2(x)-3){\sin }^2(x)y^{″}(x)+(2{\sin }^2(x)+3)\sin (x)\cos (x)y^{\prime }(x)=0$$ ✗ Mathematica : cpu = 0.222165 (sec), leaf count = 0 , could not solve

DSolve[(-3 + a^4*Sin[x]^4)*y[x] + Cos[x]*Sin[x]*(3 + 2*Sin[x]^2)*Derivative[1][y][x] + Sin[x]^2*(-3 + Sin[x]^2)*Derivative[2][y][x] + 2*Cos[x]*Sin[x]^3*Derivative[3][y][x] + Sin[x]^4*Derivative[4][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.902 (sec), leaf count = 252

$$\{y\left(x\right)=({}_2\text{F}{}_1(\frac{3}{4}-\frac{1}{4}\sqrt{-4\sqrt{-(a-1)(a+1)(a^2+1)}+5},\frac{3}{4}+\frac{1}{4}\sqrt{-4\sqrt{-(a-1)(a+1)(a^2+1)}+5};\frac{1}{2};{(\cos \left(x\right))}^2)\mathit{\_}\mathit{C}\mathit{1}+{}_2\text{F}{}_1(\frac{3}{4}+\frac{1}{4}\sqrt{4\sqrt{-(a-1)(a+1)(a^2+1)}+5},\frac{3}{4}-\frac{1}{4}\sqrt{4\sqrt{-(a-1)(a+1)(a^2+1)}+5};\frac{1}{2};{(\cos \left(x\right))}^2)\mathit{\_}\mathit{C}\mathit{2}+\cos \left(x\right)({}_2\text{F}{}_1(\frac{5}{4}+\frac{1}{4}\sqrt{-4\sqrt{-(a-1)(a+1)(a^2+1)}+5},\frac{5}{4}-\frac{1}{4}\sqrt{-4\sqrt{-(a-1)(a+1)(a^2+1)}+5};\frac{3}{2};{(\cos \left(x\right))}^2)\mathit{\_}\mathit{C}\mathit{3}+{}_2\text{F}{}_1(\frac{5}{4}-\frac{1}{4}\sqrt{4\sqrt{-(a-1)(a+1)(a^2+1)}+5},\frac{5}{4}+\frac{1}{4}\sqrt{4\sqrt{-(a-1)(a+1)(a^2+1)}+5};\frac{3}{2};{(\cos \left(x\right))}^2)\mathit{\_}\mathit{C}\mathit{4}))\sin \left(x\right)\}$$