60.3.38 problem 1039

Internal problem ID [11048]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1039
Date solved : Monday, January 27, 2025 at 10:42:35 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} y^{\prime \prime }+x y^{\prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(diff(y(x),x),x)+x*diff(y(x),x)+y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 41

DSolve[y[x] + x*D[y[x],x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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