4.49   ODE No. 1049

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -4\,x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) + \left ( 4\,{x}^{2}-1 \right ) y \left ( x \right ) -{{\rm e}^{x}}=0} \]

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

Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]

Maple: cpu = 0.125 (sec), leaf count = 70 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{x}^{2}}}\cos \left ( x \right ) {\it \_C2}+{{\rm e}^{{x}^{2}}}\sin \left ( x \right ) {\it \_C1}-{\frac {{{\rm e}^{{x}^{2}}} \left ( -{{\rm e}^{{\frac {i}{2}}}} \left ( i\cos \left ( x \right ) +\sin \left ( x \right ) \right ) {\it Erf} \left ( x-{ \frac {1}{2}}-{\frac {i}{2}} \right ) + \left ( i\cos \left ( x \right ) - \sin \left ( x \right ) \right ) {\it Erf} \left ( x-{\frac {1}{2}}+{ \frac {i}{2}} \right ) {{\rm e}^{-{\frac {i}{2}}}} \right ) \sqrt {\pi } }{4}} \right \} \]