4.206   ODE No. 1206

\[ \boxed { {x}^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( 2\,ax+b \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( abx+c{x}^{2}+d \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.114515 (sec), leaf count = 120 \[ \left \{\left \{y(x)\to c_1 e^{\frac {1}{2} (-2 a x-(b-1) \log (x))} J_{\frac {1}{2} \sqrt {b^2-2 b-4 d+1}}\left (-i \sqrt {a^2-c} x\right )+c_2 e^{\frac {1}{2} (-2 a x-(b-1) \log (x))} Y_{\frac {1}{2} \sqrt {b^2-2 b-4 d+1}}\left (-i \sqrt {a^2-c} x\right )\right \}\right \} \]

Maple: cpu = 0.062 (sec), leaf count = 87 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-ax}}{x}^{{\frac {1 }{2}}-{\frac {b}{2}}}{{\sl J}_{{\frac {1}{2}\sqrt {{b}^{2}-2\,b-4\,d+1 }}}\left (\sqrt {-{a}^{2}+c}x\right )}+{\it \_C2}\,{{\rm e}^{-ax}}{x}^{{ \frac {1}{2}}-{\frac {b}{2}}}{{\sl Y}_{{\frac {1}{2}\sqrt {{b}^{2}-2\, b-4\,d+1}}}\left (\sqrt {-{a}^{2}+c}x\right )} \right \} \]