4.28.25 \(a y'(x)+y(x) \left (\text {a1}+\text {b1} x+\text {c1} x^2\right )+x y''(x)=0\)

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

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✗
cpu = 1.28382 (sec), leaf count = 0 , DifferentialRoot result

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

Maple ✗
cpu = 1.299 (sec), leaf count = 0 , result contains DESol or ODESolStruc

\[[]\]

Mathematica raw input

DSolve[(a1 + b1*x + c1*x^2)*y[x] + a*y'[x] + x*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> DifferentialRoot[Function[{\[FormalY], \[FormalX]}, {(a1 + \[FormalX]*
b1 + \[FormalX]^2*c1)*\[FormalY][\[FormalX]] + a*Derivative[1][\[FormalY]][\[For
malX]] + \[FormalX]*Derivative[2][\[FormalY]][\[FormalX]] == 0, \[FormalY][1] ==
 C[1], Derivative[1][\[FormalY]][1] == C[2]}]][x]}}

Maple raw input

dsolve(x*diff(diff(y(x),x),x)+a*diff(y(x),x)+(c1*x^2+b1*x+a1)*y(x) = 0, y(x))

Maple raw output

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