ODE No. 1059

\[ x^4 y'(x)-x^3 y(x)+y''(x)=0 \] Mathematica : cpu = 0.0514939 (sec), leaf count = 39

DSolve[-(x^3*y[x]) + x^4*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 x-\frac {c_2 \sqrt [5]{x^5} \Gamma \left (-\frac {1}{5},\frac {x^5}{5}\right )}{5 \sqrt [5]{5}}\right \}\right \}\] Maple : cpu = 0.076 (sec), leaf count = 56

dsolve(diff(diff(y(x),x),x)+x^4*diff(y(x),x)-x^3*y(x)=0,y(x))
 

\[y \left (x \right ) = \frac {9 c_{2} {\mathrm e}^{-\frac {x^{5}}{10}} \left (x^{5}+4\right ) \WhittakerM \left (\frac {7}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right )+x^{8} \left (x^{2} c_{2} {\mathrm e}^{-\frac {x^{5}}{10}} \WhittakerM \left (\frac {2}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right )+c_{1}\right )}{x^{7}}\]