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 = 0.0985292 (sec), leaf count = 232

\[\left \{\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {i \sqrt {2}}{\sqrt {x^2 \sinh \left (\frac {2 c_1}{9}\right )+x^2 \cosh \left (\frac {2 c_1}{9}\right )-i}}-(1-i)}\right )\right \},\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {i \sqrt {2}}{\sqrt {x^2 \sinh \left (\frac {2 c_1}{9}\right )+x^2 \cosh \left (\frac {2 c_1}{9}\right )-i}}}\right )\right \},\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{(-1+i)-\frac {\sqrt {2}}{\sqrt {x^2 \sinh \left (\frac {2 c_1}{9}\right )+x^2 \cosh \left (\frac {2 c_1}{9}\right )+i}}}\right )\right \},\left \{y(x)\to x^2 \left (1+\frac {2-2 i}{\frac {\sqrt {2}}{\sqrt {x^2 \sinh \left (\frac {2 c_1}{9}\right )+x^2 \cosh \left (\frac {2 c_1}{9}\right )+i}}-(1-i)}\right )\right \}\right \}\]

Maple : cpu = 0.203 (sec), leaf count = 57

\[ \left \{ y \left ( x \right ) =-{\frac {{\it \_C1}}{2}\sqrt {{{\it \_C1}}^{2}-4\,{x}^{2}}}+{\frac {{{\it \_C1}}^{2}}{2}}-{x}^{2},y \left ( x \right ) ={\frac {{\it \_C1}}{2}\sqrt {{{\it \_C1}}^{2}-4\,{x}^{2}}}+{\frac {{{\it \_C1}}^{2}}{2}}-{x}^{2} \right \} \]