2.1670   ODE No. 1670

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ a \left (x y'(x)-y(x)\right )^2-b+x y''(x)=0 \] Mathematica : cpu = 7.64263 (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 = 1.733 (sec), leaf count = 35

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