ODE No. 1638

$$a{y}^{\prime }(x{)}^2+b\sin (y(x))+y^{″}(x)=0$$ ✓ Mathematica : cpu = 3.87742 (sec), leaf count = 146

DSolve[b*Sin[y[x]] + a*Derivative[1][y][x]^2 + Derivative[2][y][x] == 0,y[x],x]
 

$$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{\sqrt{4a^2+1}}{\sqrt{4e^{-2aK[1]}{c}_1{a}^2-4b\sin (K[1])a+e^{-2aK[1]}{c}_1+2b\cos (K[1])}}dK[1]\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{\sqrt{4a^2+1}}{\sqrt{4e^{-2aK[2]}{c}_1{a}^2-4b\sin (K[2])a+e^{-2aK[2]}{c}_1+2b\cos (K[2])}}dK[2]\mathrm{\&}][x+c_2]\}\}$$ ✓ Maple : cpu = 0.227 (sec), leaf count = 115

dsolve(diff(diff(y(x),x),x)+a*diff(y(x),x)^2+b*sin(y(x))=0,y(x))
 

$${\int }_{}^{y\left(x\right)}\frac{4a^2+1}{\sqrt{16c_1{(a^2+\frac{1}{4})}^2{\mathrm{e}}^{-2a\mathit{\text{\_a}}}-16b(a\sin \left(\mathit{\text{\_a}}\right)-\frac{\cos \left(\mathit{\text{\_a}}\right)}{2})(a^2+\frac{1}{4})}}d\mathit{\text{\_a}}-x-c_2=0$$