60.3.39 problem 1040

Internal problem ID [11049]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1040
Date solved : Monday, January 27, 2025 at 10:42:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.131 (sec). Leaf size: 45

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

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