2.164   ODE No. 164

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

\[ 2 a^2 x+2 x^2 y'(x)-2 y(x)^2-3 x y(x)=0 \] Mathematica : cpu = 0.0791822 (sec), leaf count = 76

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

Maple : cpu = 0.217 (sec), leaf count = 102

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