4.46.14 \(x^4 y''''(x)+8 x^3 y'''(x)+a y(x)+12 x^2 y''(x)=0\)

ODE
\[ x^4 y''''(x)+8 x^3 y'''(x)+a y(x)+12 x^2 y''(x)=0 \] ODE Classification

[[_high_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0145875 (sec), leaf count = 116

\[\left \{\left \{y(x)\to \frac {c_1 x^{-\frac {1}{2} \sqrt {5-4 \sqrt {1-a}}}+c_2 x^{\frac {1}{2} \sqrt {5-4 \sqrt {1-a}}}+c_3 x^{-\frac {1}{2} \sqrt {4 \sqrt {1-a}+5}}+c_4 x^{\frac {1}{2} \sqrt {4 \sqrt {1-a}+5}}}{\sqrt {x}}\right \}\right \}\]

Maple ✓
cpu = 0.027 (sec), leaf count = 89

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{-{\frac {1}{2}}-{\frac {1}{2}\sqrt {5-4\,\sqrt {1-a}}}}+{\it \_C2}\,{x}^{-{\frac {1}{2}}+{\frac {1}{2}\sqrt {5-4\,\sqrt {1-a}}}}+{\it \_C3}\,{x}^{-{\frac {1}{2}}-{\frac {1}{2}\sqrt {5+4\,\sqrt {1-a}}}}+{\it \_C4}\,{x}^{-{\frac {1}{2}}+{\frac {1}{2}\sqrt {5+4\,\sqrt {1-a}}}} \right \} \] Mathematica raw input

DSolve[a*y[x] + 12*x^2*y''[x] + 8*x^3*y'''[x] + x^4*y''''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (C[1]/x^(Sqrt[5 - 4*Sqrt[1 - a]]/2) + x^(Sqrt[5 - 4*Sqrt[1 - a]]/2)*C[
2] + C[3]/x^(Sqrt[5 + 4*Sqrt[1 - a]]/2) + x^(Sqrt[5 + 4*Sqrt[1 - a]]/2)*C[4])/Sq
rt[x]}}

Maple raw input

dsolve(x^4*diff(diff(diff(diff(y(x),x),x),x),x)+8*x^3*diff(diff(diff(y(x),x),x),x)+12*x^2*diff(diff(y(x),x),x)+a*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*x^(-1/2-1/2*(5-4*(1-a)^(1/2))^(1/2))+_C2*x^(-1/2+1/2*(5-4*(1-a)^(1/2)
)^(1/2))+_C3*x^(-1/2-1/2*(5+4*(1-a)^(1/2))^(1/2))+_C4*x^(-1/2+1/2*(5+4*(1-a)^(1/
2))^(1/2))