ODE
\[ 4 (1-x) x (1-a x) y''(x)+y'(x) \left (\text {a0}+\text {a1} x+\text {a2} x^2\right )+y(x) \left (\text {b0}+\text {b1} x^2\right )=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries]]
Book solution method
TO DO
Mathematica ✗
cpu = 6.09979 (sec), leaf count = 0 , DifferentialRoot result
\[\left \{\left \{y(x)\to (x)\right \}\right \}\]
Maple ✗
cpu = 3.628 (sec), leaf count = 0 , result contains DESol or ODESolStruc
\[[]\]
Mathematica raw input
DSolve[(b0 + b1*x^2)*y[x] + (a0 + a1*x + a2*x^2)*y'[x] + 4*(1 - x)*x*(1 - a*x)*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> DifferentialRoot[Function[{\[FormalY], \[FormalX]}, {(b0 + \[FormalX]^2*b1)*\[FormalY][\[FormalX]] + (a0 + \[FormalX]*a1 + \[FormalX]^2*a2)*Derivative[1][\[FormalY]][\[FormalX]] + 4*(-1 + \[FormalX])*\[FormalX]*(-1 + \[FormalX]*a)*Derivative[2][\[FormalY]][\[FormalX]] == 0, \[FormalY][2] == C[1], Derivative[1][\[FormalY]][2] == C[2]}]][x]}}
Maple raw input
dsolve(4*x*(1-x)*(-a*x+1)*diff(diff(y(x),x),x)+(a2*x^2+a1*x+a0)*diff(y(x),x)+(b1*x^2+b0)*y(x) = 0, y(x))
Maple raw output
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