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 = 26.4505 (sec), leaf count = 176

$$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{\sqrt{2}\sqrt{\cos (2K[1])a-a-2b}}{\sqrt{2aAK[1{]}^2+4AcK[1{]}^2-2aA\sin (2K[1])K[1]+2c_1-aA\cos (2K[1])}}dK[1]\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{\sqrt{2}\sqrt{\cos (2K[2])a-a-2b}}{\sqrt{2aAK[2{]}^2+4AcK[2{]}^2-2aA\sin (2K[2])K[2]+2c_1-aA\cos (2K[2])}}dK[2]\mathrm{\&}][x+c_2]\}\}$$ ✓ Maple : cpu = 0.944 (sec), leaf count = 138

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