4.29.22 \(x^2 y''(x)=6 y(x)\)

ODE
\[ x^2 y''(x)=6 y(x) \] ODE Classification

[[_Emden, _Fowler]]

Book solution method
TO DO

Mathematica
cpu = 0.160546 (sec), leaf count = 18

\[\left \{\left \{y(x)\to \frac {c_2 x^5+c_1}{x^2}\right \}\right \}\]

Maple
cpu = 0.014 (sec), leaf count = 15

\[\left [y \left (x \right ) = \frac {\textit {\_C1}}{x^{2}}+\textit {\_C2} \,x^{3}\right ]\] Mathematica raw input

DSolve[x^2*y''[x] == 6*y[x],y[x],x]

Mathematica raw output

{{y[x] -> (C[1] + x^5*C[2])/x^2}}

Maple raw input

dsolve(x^2*diff(diff(y(x),x),x) = 6*y(x), y(x))

Maple raw output

[y(x) = _C1/x^2+_C2*x^3]