2.218   ODE No. 218

\[ \left (y(x)-x^2\right ) y'(x)+4 x y(x)=0 \] Mathematica : cpu = 0.140635 (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 = 0.162 (sec), leaf count = 57


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