2.1040   ODE No. 1040

\[ y''(x)+x y'(x)-y(x)=0 \]

✓ Mathematica : cpu = 0.0560492 (sec), leaf count = 53

DSolve[-y[x] + x*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 x-\frac {1}{2} c_2 e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } e^{\frac {x^2}{2}} x \text {erf}\left (\frac {x}{\sqrt {2}}\right )+2\right )\right \}\right \}\]

✓ Maple : cpu = 0.065 (sec), leaf count = 33

dsolve(diff(diff(y(x),x),x)+x*diff(y(x),x)-y(x)=0,y(x))
 

\[y \left (x \right ) = \sqrt {\pi }\, \sqrt {2}\, {\mathrm e}^{-\frac {x^{2}}{2}} c_{2} +x \left (\pi c_{2} \operatorname {erf}\left (\frac {x \sqrt {2}}{2}\right )+c_{1} \right )\]