4.36.8 \(x \left (a^2-x^2\right ) \left (b^2-x^2\right ) y''(x)+\left (\text {a0}+\text {b0} x^4\right ) y'(x)+x^3 y(x) \left (\text {a1}+\text {b1} x^2+\text {c1} x^4\right )=0\)

ODE
\[ x \left (a^2-x^2\right ) \left (b^2-x^2\right ) y''(x)+\left (\text {a0}+\text {b0} x^4\right ) y'(x)+x^3 y(x) \left (\text {a1}+\text {b1} x^2+\text {c1} x^4\right )=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✗
cpu = 84.7687 (sec), leaf count = 0 , DifferentialRoot result

\[\left \{\left \{y(x)\to (x)\right \}\right \}\]

Maple ✗
cpu = 7.239 (sec), leaf count = 0 , result contains DESol or ODESolStruc

\[[]\]

Mathematica raw input

DSolve[x^3*(a1 + b1*x^2 + c1*x^4)*y[x] + (a0 + b0*x^4)*y'[x] + x*(a^2 - x^2)*(b^2 - x^2)*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> DifferentialRoot[Function[{\[FormalY], \[FormalX]}, {(\[FormalX]^3*a1 
+ \[FormalX]^5*b1 + \[FormalX]^7*c1)*\[FormalY][\[FormalX]] + (a0 + \[FormalX]^4
*b0)*Derivative[1][\[FormalY]][\[FormalX]] + \[FormalX]*(-\[FormalX] + a)*(\[For
malX] + a)*(-\[FormalX] + b)*(\[FormalX] + b)*Derivative[2][\[FormalY]][\[Formal
X]] == 0, \[FormalY][1] == C[1], Derivative[1][\[FormalY]][1] == C[2]}]][x]}}

Maple raw input

dsolve(x*(a^2-x^2)*(b^2-x^2)*diff(diff(y(x),x),x)+(b0*x^4+a0)*diff(y(x),x)+x^3*(c1*x^4+b1*x^2+a1)*y(x) = 0, y(x))

Maple raw output

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