ODE No. 1640

$$ay(x)y^{\prime }(x{)}^2+by(x)+y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.452445 (sec), leaf count = 96

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

$$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}-\frac{\sqrt{a}}{\sqrt{e^{2a{c}_1-aK[1{]}^2}-b}}dK[1]\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{\sqrt{a}}{\sqrt{e^{2a{c}_1-aK[2{]}^2}-b}}dK[2]\mathrm{\&}][x+c_2]\}\}$$ ✓ Maple : cpu = 0.987 (sec), leaf count = 70

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

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