2.143   ODE No. 143

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

✓ Mathematica : cpu = 0.0851445 (sec), leaf count = 51

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

\[\left \{\left \{y(x)\to -\frac {-1+\sqrt {4 a b+1} \left (-1+\frac {2 c_1}{x^{\sqrt {4 a b+1}}+c_1}\right )}{2 a x}\right \}\right \}\]

✓ Maple : cpu = 0.07 (sec), leaf count = 41

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

\[y \left (x \right ) = \frac {1-\tanh \left (\frac {\sqrt {4 a b +1}\, \left (-\ln \left (x \right )+c_{1} \right )}{2}\right ) \sqrt {4 a b +1}}{2 a x}\]