2.1190   ODE No. 1190

\[ y(x) (a x+b)+x^2 y''(x)+x^2 y'(x)=0 \]

✓ Mathematica : cpu = 0.0164096 (sec), leaf count = 122

DSolve[(b + a*x)*y[x] + x^2*Derivative[1][y][x] + x^2*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 e^{\frac {1}{2} \left (\left (\sqrt {1-4 b}+1\right ) \log (x)-2 x\right )} U\left (\frac {1}{2} \left (-2 a+\sqrt {1-4 b}+1\right ),\sqrt {1-4 b}+1,x\right )+c_2 e^{\frac {1}{2} \left (\left (\sqrt {1-4 b}+1\right ) \log (x)-2 x\right )} L_{\frac {1}{2} \left (2 a-\sqrt {1-4 b}-1\right )}^{\sqrt {1-4 b}}(x)\right \}\right \}\]

✓ Maple : cpu = 0.153 (sec), leaf count = 38

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

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