ODE No. 209

\[ y(x) y'(x)-\sqrt {a y(x)^2+b}=0 \] Mathematica : cpu = 0.122002 (sec), leaf count = 84

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

\[\left \{\left \{y(x)\to -\frac {\sqrt {a^2 x^2+2 a^2 c_1 x+a^2 c_1{}^2-b}}{\sqrt {a}}\right \},\left \{y(x)\to \frac {\sqrt {a^2 x^2+2 a^2 c_1 x+a^2 c_1{}^2-b}}{\sqrt {a}}\right \}\right \}\] Maple : cpu = 0.015 (sec), leaf count = 21

dsolve(y(x)*diff(y(x),x)-(a*y(x)^2+b)^(1/2) = 0,y(x))
 

\[x -\frac {\sqrt {a y \left (x \right )^{2}+b}}{a}+c_{1} = 0\]