ODE
\[ x^4 y''''(x)+8 x^3 y'''(x)+12 x^2 y''(x)=0 \] ODE Classification
[[_high_order, _missing_y]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0268161 (sec), leaf count = 27
\[\left \{\left \{y(x)\to \frac {3 c_2 x+c_1}{6 x^2}+c_4 x+c_3\right \}\right \}\]
Maple ✓
cpu = 0.012 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\it \_C1}+{\frac {{\it \_C2}}{x}}+{\it \_C3}\,x+{\frac {{\it \_C4}}{{x}^{2}}} \right \} \] Mathematica raw input
DSolve[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] + 3*x*C[2])/(6*x^2) + C[3] + x*C[4]}}
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) = 0, y(x),'implicit')
Maple raw output
y(x) = _C1+_C2/x+_C3*x+_C4/x^2