2.181   ODE No. 181

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

\[ a+x^4 \left (y'(x)+y(x)^2\right )=0 \] Mathematica : cpu = 0.0123108 (sec), leaf count = 100

\[\left \{\left \{y(x)\to \frac {\left (x+i \sqrt {-a} c_1\right ) \cosh \left (\frac {\sqrt {-a}}{x}\right )-\left (\sqrt {-a}+i c_1 x\right ) \sinh \left (\frac {\sqrt {-a}}{x}\right )}{x^2 \left (\cosh \left (\frac {\sqrt {-a}}{x}\right )-i c_1 \sinh \left (\frac {\sqrt {-a}}{x}\right )\right )}\right \}\right \}\]

Maple : cpu = 0.082 (sec), leaf count = 28

\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{2}} \left ( -\tan \left ( {\frac {{\it \_C1}\,x-1}{x}\sqrt {a}} \right ) \sqrt {a}+x \right ) } \right \} \]