ODE No. 1154

\[ y(x) \left (a x^2+b x+c\right )+x^2 y''(x)=0 \] Mathematica : cpu = 0.0139399 (sec), leaf count = 88

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

\[\left \{\left \{y(x)\to c_1 M_{-\frac {i b}{2 \sqrt {a}},-\frac {1}{2} i \sqrt {4 c-1}}\left (2 i \sqrt {a} x\right )+c_2 W_{-\frac {i b}{2 \sqrt {a}},-\frac {1}{2} i \sqrt {4 c-1}}\left (2 i \sqrt {a} x\right )\right \}\right \}\] Maple : cpu = 0.112 (sec), leaf count = 57

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

\[y \left (x \right ) = c_{1} \WhittakerM \left (-\frac {i b}{2 \sqrt {a}}, \frac {\sqrt {1-4 c}}{2}, 2 i \sqrt {a}\, x \right )+c_{2} \WhittakerW \left (-\frac {i b}{2 \sqrt {a}}, \frac {\sqrt {1-4 c}}{2}, 2 i \sqrt {a}\, x \right )\]