2.1813   ODE No. 1813

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

$$Ay(x)(a{\sin }^2(y(x))+c)+y^{″}(x)(a{\sin }^2(y(x))+b)+a{y}^{\prime }(x{)}^2\sin (y(x))\cos (y(x))=0$$ ✗ Mathematica : cpu = 103.094 (sec), leaf count = 0 , could not solve

DSolve[A*(c + a*Sin[y[x]]^2)*y[x] + a*Cos[y[x]]*Sin[y[x]]*Derivative[1][y][x]^2 + (b + a*Sin[y[x]]^2)*Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.638 (sec), leaf count = 138

$$\{{\int }^{y\left(x\right)}\sqrt{2}(b+a{(\sin \left(\mathit{\_}\mathit{a}\right))}^2)\frac{1}{\sqrt{-(b+a{(\sin \left(\mathit{\_}\mathit{a}\right))}^2)(A{(\sin \left(\mathit{\_}\mathit{a}\right))}^{2}a-2A\cos \left(\mathit{\_}\mathit{a}\right)\sin \left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{a}a+{\mathit{\_}\mathit{a}}^2(a+2c)A-2\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\sqrt{2}(b+a{(\sin \left(\mathit{\_}\mathit{a}\right))}^2)\frac{1}{\sqrt{-(b+a{(\sin \left(\mathit{\_}\mathit{a}\right))}^2)(A{(\sin \left(\mathit{\_}\mathit{a}\right))}^{2}a-2A\cos \left(\mathit{\_}\mathit{a}\right)\sin \left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{a}a+{\mathit{\_}\mathit{a}}^2(a+2c)A-2\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$