2.536   ODE No. 536

\[ b x \left (x^2-a^2\right ) y'(x)^2+\left (x^2-a^2\right ) y'(x)^3+b x+y'(x)=0 \]

✓ Mathematica : cpu = 0.0258429 (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]
 

\[\left \{\left \{y(x)\to -\frac {b x^2}{2}+c_1\right \},\left \{y(x)\to -\tan ^{-1}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1\right \},\left \{y(x)\to \tan ^{-1}\left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1\right \}\right \}\]

✓ Maple : cpu = 0.034 (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))
 

\[y \left (x \right ) = -\frac {b \,x^{2}}{2}+c_{1}\]