2.218   ODE No. 218

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

\[ \left (y(x)-x^2\right ) y'(x)+4 x y(x)=0 \] Mathematica : cpu = 0.152185 (sec), leaf count = 257

\[\left \{\left \{y(x)\to x^2+\frac {1}{-\frac {1}{2 x^2}-\frac {\frac {1}{2}-\frac {i}{2}}{\sqrt {2} x^2 \sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )-i}}}\right \},\left \{y(x)\to x^2+\frac {1}{-\frac {1}{2 x^2}+\frac {\frac {1}{2}-\frac {i}{2}}{\sqrt {2} x^2 \sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )-i}}}\right \},\left \{y(x)\to x^2+\frac {1}{-\frac {1}{2 x^2}-\frac {\frac {1}{2}+\frac {i}{2}}{\sqrt {2} x^2 \sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )+i}}}\right \},\left \{y(x)\to x^2+\frac {1}{-\frac {1}{2 x^2}+\frac {\frac {1}{2}+\frac {i}{2}}{\sqrt {2} x^2 \sqrt {x^2 \cosh \left (\frac {2 c_1}{9}\right )+x^2 \sinh \left (\frac {2 c_1}{9}\right )+i}}}\right \}\right \}\] Maple : cpu = 0.169 (sec), leaf count = 57

\[\left \{y \left (x \right ) = \frac {c_{1}^{2}}{2}-x^{2}-\frac {c_{1} \sqrt {-4 x^{2}+c_{1}^{2}}}{2}, y \left (x \right ) = \frac {c_{1}^{2}}{2}-x^{2}+\frac {c_{1} \sqrt {-4 x^{2}+c_{1}^{2}}}{2}\right \}\]