3.218   ODE No. 218

\[ \boxed { \left ( y \left ( x \right ) -{x}^{2} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +4\,xy \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.102513 (sec), leaf count = 257 \[ \left \{\left \{y(x)\to x^2+\frac {1}{-\frac {1}{2 x^2}-\frac {\frac {1}{2}-\frac {i}{2}}{\sqrt {2} x^2 \sqrt {x^2 \sinh \left (\frac {2 c_1}{9}\right )+x^2 \cosh \left (\frac {2 c_1}{9}\right )-i}}}\right \},\left \{y(x)\to x^2+\frac {1}{-\frac {1}{2 x^2}+\frac {\frac {1}{2}-\frac {i}{2}}{\sqrt {2} x^2 \sqrt {x^2 \sinh \left (\frac {2 c_1}{9}\right )+x^2 \cosh \left (\frac {2 c_1}{9}\right )-i}}}\right \},\left \{y(x)\to x^2+\frac {1}{-\frac {1}{2 x^2}-\frac {\frac {1}{2}+\frac {i}{2}}{\sqrt {2} x^2 \sqrt {x^2 \sinh \left (\frac {2 c_1}{9}\right )+x^2 \cosh \left (\frac {2 c_1}{9}\right )+i}}}\right \},\left \{y(x)\to x^2+\frac {1}{-\frac {1}{2 x^2}+\frac {\frac {1}{2}+\frac {i}{2}}{\sqrt {2} x^2 \sqrt {x^2 \sinh \left (\frac {2 c_1}{9}\right )+x^2 \cosh \left (\frac {2 c_1}{9}\right )+i}}}\right \}\right \} \]

Maple: cpu = 0.140 (sec), leaf count = 53 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}}{2} \left ( {\it \_C1}- \sqrt {{{\it \_C1}}^{2}-4\,{x}^{2}} \right ) }-{x}^{2},y \left ( x \right ) ={\frac {{\it \_C1}}{2} \left ( {\it \_C1}+\sqrt {{{\it \_C1}} ^{2}-4\,{x}^{2}} \right ) }-{x}^{2} \right \} \]