2.1059   ODE No. 1059

\[ x^4 y'(x)-x^3 y(x)+y''(x)=0 \]

✓ Mathematica : cpu = 0.0960131 (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 = 0.108 (sec), leaf count = 55

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

\[y \left (x \right ) = x c_{1} +\frac {c_{2} {\mathrm e}^{-\frac {x^{5}}{10}} \left (x^{10} \operatorname {WhittakerM}\left (\frac {2}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right )+9 \operatorname {WhittakerM}\left (\frac {7}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right ) x^{5}+36 \operatorname {WhittakerM}\left (\frac {7}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right )\right )}{x^{7}}\]