4.29.32 \(y(x) \left (a+b x+c x^2\right )+x^2 y''(x)=0\)

ODE
\[ y(x) \left (a+b x+c x^2\right )+x^2 y''(x)=0 \] ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0177698 (sec), leaf count = 88

\[\left \{\left \{y(x)\to c_1 M_{-\frac {i b}{2 \sqrt {c}},-\frac {1}{2} i \sqrt {4 a-1}}\left (2 i \sqrt {c} x\right )+c_2 W_{-\frac {i b}{2 \sqrt {c}},-\frac {1}{2} i \sqrt {4 a-1}}\left (2 i \sqrt {c} x\right )\right \}\right \}\]

Maple ✓
cpu = 0.151 (sec), leaf count = 57

\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\sl M}_{{-{\frac {i}{2}}b{\frac {1}{\sqrt {c}}}},\,{\frac {1}{2}\sqrt {1-4\,a}}}\left (2\,i\sqrt {c}x\right )}+{\it \_C2}\,{{\sl W}_{{-{\frac {i}{2}}b{\frac {1}{\sqrt {c}}}},\,{\frac {1}{2}\sqrt {1-4\,a}}}\left (2\,i\sqrt {c}x\right )} \right \} \] Mathematica raw input

DSolve[(a + b*x + c*x^2)*y[x] + x^2*y''[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> C[1]*WhittakerM[((-I/2)*b)/Sqrt[c], (-I/2)*Sqrt[-1 + 4*a], (2*I)*Sqrt[
c]*x] + C[2]*WhittakerW[((-I/2)*b)/Sqrt[c], (-I/2)*Sqrt[-1 + 4*a], (2*I)*Sqrt[c]
*x]}}

Maple raw input

dsolve(x^2*diff(diff(y(x),x),x)+(c*x^2+b*x+a)*y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = _C1*WhittakerM(-1/2*I*b/c^(1/2),1/2*(1-4*a)^(1/2),2*I*c^(1/2)*x)+_C2*Whit
takerW(-1/2*I*b/c^(1/2),1/2*(1-4*a)^(1/2),2*I*c^(1/2)*x)