8.223   ODE No. 1813

$$\boxed{{\displaystyle (b+a{(\sin \left(y\left(x\right)\right))}^2)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+a{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2\cos \left(y\left(x\right)\right)\sin \left(y\left(x\right)\right)+Ay\left(x\right)(c+a{(\sin \left(y\left(x\right)\right))}^2)=0}}$$

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

Mathematica: cpu = 100.860808 (sec), leaf count = 48 $$\text{DSolve}[Ay(x)(a{\sin }^2(y(x))+c)+y^{″}(x)(a{\sin }^2(y(x))+b)+a{y}^{\prime }(x{)}^2\sin (y(x))\cos (y(x))=0,y(x),x]$$

Maple: cpu = 0.265 (sec), leaf count = 146 $$\{{\int }^{y\left(x\right)}\sqrt{2}(b+a{(\sin \left(\mathit{\_}\mathit{a}\right))}^2)\frac{1}{\sqrt{(b+a{(\sin \left(\mathit{\_}\mathit{a}\right))}^2)(2Aa\mathit{\_}\mathit{a}\cos \left(\mathit{\_}\mathit{a}\right)\sin \left(\mathit{\_}\mathit{a}\right)-Aa{(\sin \left(\mathit{\_}\mathit{a}\right))}^2-Aa{\mathit{\_}\mathit{a}}^2-2Ac{\mathit{\_}\mathit{a}}^2+2\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\sqrt{2}(b+a{(\sin \left(\mathit{\_}\mathit{a}\right))}^2)\frac{1}{\sqrt{(b+a{(\sin \left(\mathit{\_}\mathit{a}\right))}^2)(2Aa\mathit{\_}\mathit{a}\cos \left(\mathit{\_}\mathit{a}\right)\sin \left(\mathit{\_}\mathit{a}\right)-Aa{(\sin \left(\mathit{\_}\mathit{a}\right))}^2-Aa{\mathit{\_}\mathit{a}}^2-2Ac{\mathit{\_}\mathit{a}}^2+2\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$