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

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

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.200065 (sec), leaf count = 39

\[\left \{\left \{y(x)\to c_1 x-\frac {c_2 \sqrt [5]{x^5} \Gamma \left (-\frac {1}{5},\frac {x^5}{5}\right )}{5 \sqrt [5]{5}}\right \}\right \}\]

Maple ✓
cpu = 0.231 (sec), leaf count = 55

\[\left [y \left (x \right ) = \textit {\_C1} x +\frac {\textit {\_C2} \,{\mathrm e}^{-\frac {x^{5}}{10}} \left (x^{10} \WhittakerM \left (\frac {2}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right )+9 \WhittakerM \left (\frac {7}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right ) x^{5}+36 \WhittakerM \left (\frac {7}{5}, \frac {9}{10}, \frac {x^{5}}{5}\right )\right )}{x^{7}}\right ]\] Mathematica raw input

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

Mathematica raw output

{{y[x] -> x*C[1] - ((x^5)^(1/5)*C[2]*Gamma[-1/5, x^5/5])/(5*5^(1/5))}}

Maple raw input

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

Maple raw output

[y(x) = _C1*x+_C2/x^7*exp(-1/10*x^5)*(x^10*WhittakerM(2/5,9/10,1/5*x^5)+9*Whitta
kerM(7/5,9/10,1/5*x^5)*x^5+36*WhittakerM(7/5,9/10,1/5*x^5))]