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 = 0.0529286 (sec), leaf count = 49
\[\left \{\left \{y(x)\to -c_2 e^{-\frac {x^5}{5}}+\frac {c_2 \sqrt [5]{x^5} \Gamma \left (\frac {4}{5},\frac {x^5}{5}\right )}{\sqrt [5]{5}}+c_1 x\right \}\right \}\]
Maple ✓
cpu = 0.107 (sec), leaf count = 56
\[ \left \{ y \left ( x \right ) ={\frac {1}{{x}^{7}} \left ( 9\,{\it \_C2}\,{{\rm e}^{-1/10\,{x}^{5}}} \left ( {x}^{5}+4 \right ) {{\sl M}_{7/5,\,{\frac {9}{10}}}\left (1/5\,{x}^{5}\right )}+{x}^{8} \left ( {x}^{2}{\it \_C2}\,{{\rm e}^{-{\frac {{x}^{5}}{10}}}}{{\sl M}_{{\frac {2}{5}},\,{\frac {9}{10}}}\left ({\frac {{x}^{5}}{5}}\right )}+{\it \_C1} \right ) \right ) } \right \} \] 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] - C[2]/E^(x^5/5) + ((x^5)^(1/5)*C[2]*Gamma[4/5, x^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),'implicit')
Maple raw output
y(x) = (9*_C2*exp(-1/10*x^5)*(x^5+4)*WhittakerM(7/5,9/10,1/5*x^5)+x^8*(x^2*_C2*exp(-1/10*x^5)*WhittakerM(2/5,9/10,1/5*x^5)+_C1))/x^7