4.346   ODE No. 1346

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

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

Mathematica: cpu = 0.326541 (sec), leaf count = 87 \[ \left \{\left \{y(x)\to c_1 x e^{-\frac {-\sqrt {(a-b)^2}+a+b}{2 x}}+\frac {c_2 x e^{-\frac {\sqrt {(a-b)^2}}{2 x}-\frac {a}{2 x}-\frac {b}{2 x}}}{\sqrt {(a-b)^2}}\right \}\right \} \]

Maple: cpu = 0.047 (sec), leaf count = 25 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,x{{\rm e}^{-{\frac {a}{x}}}}+ {\it \_C2}\,x{{\rm e}^{-{\frac {b}{x}}}} \right \} \]