#### 2.181   ODE No. 181

$a+x^4 \left (y'(x)+y(x)^2\right )=0$ Mathematica : cpu = 0.0846795 (sec), leaf count = 347

$\left \{\left \{y(x)\to -\frac {\frac {i \sqrt {\frac {2}{\pi }} c_1 \sinh \left (\frac {\sqrt {-a}}{x}\right )}{\sqrt {-\frac {i \sqrt {-a}}{x}}}+\frac {i \sqrt {-a} \left (-\frac {2 \sqrt {\frac {2}{\pi }} \left (i \sinh \left (\frac {\sqrt {-a}}{x}\right )+\frac {i \sqrt {-a} x \cosh \left (\frac {\sqrt {-a}}{x}\right )}{a}\right )}{\sqrt {-\frac {i \sqrt {-a}}{x}}}-\frac {\sqrt {\frac {2}{\pi }} c_1 \cosh \left (\frac {\sqrt {-a}}{x}\right )}{\sqrt {-\frac {i \sqrt {-a}}{x}}}+\frac {\sqrt {\frac {2}{\pi }} c_1 \left (-\frac {\sqrt {-a} x \sinh \left (\frac {\sqrt {-a}}{x}\right )}{a}-\cosh \left (\frac {\sqrt {-a}}{x}\right )\right )}{\sqrt {-\frac {i \sqrt {-a}}{x}}}\right )}{x}}{2 x \left (\frac {\sqrt {\frac {2}{\pi }} \cosh \left (\frac {\sqrt {-a}}{x}\right )}{\sqrt {-\frac {i \sqrt {-a}}{x}}}-\frac {i \sqrt {\frac {2}{\pi }} c_1 \sinh \left (\frac {\sqrt {-a}}{x}\right )}{\sqrt {-\frac {i \sqrt {-a}}{x}}}\right )}\right \}\right \}$ Maple : cpu = 0.054 (sec), leaf count = 28

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