ODE
\[ \left (a^2+x^2\right )^2 \left (b^2+x^2\right ) y''(x)+x \left (\text {a0}+\text {b0} x^2\right ) y'(x)+y(x) \left (\text {a1}+\text {b1} x^2\right )=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 133.648 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to (x)\right \}\right \}\]
Maple ✗
cpu = 6.647 (sec), leaf count = 0 , result contains DESol or ODESolStruc
\[[]\]
Mathematica raw input
DSolve[(a1 + b1*x^2)*y[x] + x*(a0 + b0*x^2)*y'[x] + (a^2 + x^2)^2*(b^2 + x^2)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> DifferentialRoot[Function[{\[FormalY], \[FormalX]}, {(a1 + \[FormalX]^2*b1)*\[FormalY][\[FormalX]] + (\[FormalX]*a0 + \[FormalX]^3*b0)*Derivative[1][\[FormalY]][\[FormalX]] + (\[FormalX]^2 + a^2)^2*(\[FormalX]^2 + b^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*(b^2+x^2)*diff(diff(y(x),x),x)+x*(b0*x^2+a0)*diff(y(x),x)+(b1*x^2+a1)*y(x) = 0, y(x))
Maple raw output
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