8.48   ODE No. 1638

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

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

Mathematica: cpu = 100.155218 (sec), leaf count = 24 $$\text{DSolve}[a{y}^{\prime }(x{)}^2+b\sin (y(x))+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.125 (sec), leaf count = 126 $$\{{\int }^{y\left(x\right)}(4a^2+1)\frac{1}{\sqrt{(4a^2+1)(4{\mathrm{e}}^{-2a\mathit{\_}\mathit{a}}\mathit{\_}\mathit{C}\mathit{1}{a}^2-4\sin \left(\mathit{\_}\mathit{a}\right)ab+2b\cos \left(\mathit{\_}\mathit{a}\right)+{\mathrm{e}}^{-2a\mathit{\_}\mathit{a}}\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-(4a^2+1)\frac{1}{\sqrt{(4a^2+1)(4{\mathrm{e}}^{-2a\mathit{\_}\mathit{a}}\mathit{\_}\mathit{C}\mathit{1}{a}^2-4\sin \left(\mathit{\_}\mathit{a}\right)ab+2b\cos \left(\mathit{\_}\mathit{a}\right)+{\mathrm{e}}^{-2a\mathit{\_}\mathit{a}}\mathit{\_}\mathit{C}\mathit{1})}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$