ODE No. 536

$$bx(x^2-a^2)y^{\prime }(x{)}^2+(x^2-a^2)y^{\prime }(x{)}^3+bx+y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0117279 (sec), leaf count = 64

DSolve[b*x + Derivative[1][y][x] + b*x*(-a^2 + x^2)*Derivative[1][y][x]^2 + (-a^2 + x^2)*Derivative[1][y][x]^3 == 0,y[x],x]
 

$$\{\{y(x)\to -\frac{b{x}^2}{2}+c_1\},\{y(x)\to -{\tan }^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)+c_1\},\{y(x)\to {\tan }^{-1}\left(\frac{x}{\sqrt{a^2-x^2}}\right)+c_1\}\}$$ ✓ Maple : cpu = 0.043 (sec), leaf count = 52

dsolve((-a^2+x^2)*diff(y(x),x)^3+b*x*(-a^2+x^2)*diff(y(x),x)^2+diff(y(x),x)+b*x=0,y(x))
 

$$y\left(x\right)=-\frac{b{x}^2}{2}+c_1$$