2.1049   ODE No. 1049

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

\[ \left (4 x^2-1\right ) y(x)-4 x y'(x)+y''(x)-e^x=0 \] Mathematica : cpu = 0.0532486 (sec), leaf count = 109

\[\left \{\left \{y(x)\to \frac {1}{4} \sqrt {\pi } e^{x (x-i)-\frac {i}{2}} \left (e^{2 i x} \text {erfi}\left (\left (\frac {1}{2}+\frac {i}{2}\right )-i x\right )-i e^i \text {erf}\left (-x+\left (\frac {1}{2}+\frac {i}{2}\right )\right )\right )+c_1 e^{x (x-i)}-\frac {1}{2} i c_2 e^{(x-i) x+2 i x}\right \}\right \}\] Maple : cpu = 0.275 (sec), leaf count = 66

\[ \left \{ y \left ( x \right ) ={\frac { \left ( \left ( i\cos \left ( x \right ) +\sin \left ( x \right ) \right ) {{\rm e}^{{\frac {i}{2}}}}\sqrt {\pi }{\it Erf} \left ( x-{\frac {1}{2}}-{\frac {i}{2}} \right ) -{{\rm e}^{-{\frac {i}{2}}}} \left ( i\cos \left ( x \right ) -\sin \left ( x \right ) \right ) \sqrt {\pi }{\it Erf} \left ( x-{\frac {1}{2}}+{\frac {i}{2}} \right ) +4\,\sin \left ( x \right ) {\it \_C1}+4\,\cos \left ( x \right ) {\it \_C2} \right ) {{\rm e}^{{x}^{2}}}}{4}} \right \} \]