2.1503   ODE No. 1503

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

\[ \left (x^2+1\right ) y^{(3)}(x)+\frac {1}{x^2}+8 x y''(x)+10 y'(x)-2 \log (x)-3=0 \] Mathematica : cpu = 0.112436 (sec), leaf count = 62

\[\left \{\left \{y(x)\to c_3-\frac {100 \left (3 c_2-1\right ) x^3+900 c_2 x+225 c_1+36 x^5-60 \left (3 x^4+10 x^2+15\right ) x \log (x)}{900 \left (x^2+1\right )^2}\right \}\right \}\]

Maple : cpu = 0.027 (sec), leaf count = 86

\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2} \left ( {x}^{2}+2 \right ) {\it \_C1}}{ \left ( {x}^{2}+1 \right ) ^{2}}}+{\frac {x \left ( {x}^{2}+3 \right ) {\it \_C2}}{ \left ( {x}^{2}+1 \right ) ^{2}}}+{\frac {{\it \_C3}}{ \left ( {x}^{2}+1 \right ) ^{2}}}+{\frac {x \left ( 45\,{x}^{4}\ln \left ( x \right ) -9\,{x}^{4}+150\,{x}^{2}\ln \left ( x \right ) -50\,{x}^{2}+225\,\ln \left ( x \right ) -225 \right ) }{225\, \left ( {x}^{2}+1 \right ) ^{2}}} \right \} \]