Internal problem ID [9372]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1039.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime } x +y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(diff(y(x),x),x)+x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\operatorname {erf}\left (\frac {i \sqrt {2}\, x}{2}\right ) c_{1} +c_{2} \right ) {\mathrm e}^{-\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 41
DSolve[y[x] + x*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-\frac {x^2}{2}} \left (\sqrt {2 \pi } c_1 \text {erfi}\left (\frac {x}{\sqrt {2}}\right )+2 c_2\right ) \]