2.1670   ODE No. 1670

\[ a \left (x y'(x)-y(x)\right )^2-b+x y''(x)=0 \] Mathematica : cpu = 6.76141 (sec), leaf count = 51


\[\left \{\left \{y(x)\to x \left (\int _1^x\frac {\sqrt {-\frac {b}{a}} \tan \left (c_1-a \sqrt {-\frac {b}{a}} K[2]\right )}{K[2]^2}dK[2]+c_2\right )\right \}\right \}\] Maple : cpu = 1.332 (sec), leaf count = 35


\[y \relax (x ) = \left (\int \frac {i \tan \left (-i \sqrt {a}\, \sqrt {b}\, x +c_{1}\right ) \sqrt {b}}{\sqrt {a}\, x^{2}}d x +c_{2}\right ) x\]