ODE
\[ \left (a^2+x^2\right )^2 y''(x)+2 x \left (a^2+2 x^2\right ) y'(x)-y(x) \left (\text {a0}+\text {a2} x^2+\text {a4} x^4\right )=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 4.61371 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to (x)\right \}\right \}\]
Maple ✗
cpu = 4.147 (sec), leaf count = 0 , result contains DESol or ODESolStruc
\[[]\]
Mathematica raw input
DSolve[-((a0 + a2*x^2 + a4*x^4)*y[x]) + 2*x*(a^2 + 2*x^2)*y'[x] + (a^2 + x^2)^2*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> DifferentialRoot[Function[{\[FormalY], \[FormalX]}, {(-a0 - \[FormalX]^2*a2 - \[FormalX]^4*a4)*\[FormalY][\[FormalX]] + (4*\[FormalX]^3 + 2*\[FormalX]*a^2)*Derivative[1][\[FormalY]][\[FormalX]] + (\[FormalX]^2 + a^2)^2*Derivative[2][\[FormalY]][\[FormalX]] == 0, \[FormalY][0] == C[1], Derivative[1][\[FormalY]][0] == C[2]}]][x]}}
Maple raw input
dsolve((a^2+x^2)^2*diff(diff(y(x),x),x)+2*x*(a^2+2*x^2)*diff(y(x),x)-(a4*x^4+a2*x^2+a0)*y(x) = 0, y(x))
Maple raw output
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