4.279   ODE No. 1279

\[ \boxed { 4\,{x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +5\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) -\ln \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.163021 (sec), leaf count = 74 \[ \left \{\left \{y(x)\to c_1 x^{\frac {1}{2} \left (\frac {\sqrt {17}}{4}-\frac {1}{4}\right )}+c_2 x^{\frac {1}{2} \left (-\frac {1}{4}-\frac {\sqrt {17}}{4}\right )}-\frac {256 (\log (x)+1)}{\left (\sqrt {17}-1\right )^2 \left (1+\sqrt {17}\right )^2}\right \}\right \} \]

Maple: cpu = 0.094 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={x}^{-{\frac {1}{8}}+{\frac {\sqrt {17}}{ 8}}}{\it \_C2}+{x}^{-{\frac {1}{8}}-{\frac {\sqrt {17}}{8}}}{\it \_C1} -\ln \left ( x \right ) -1 \right \} \]