35.7.5 problem 2

Internal problem ID [6187]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 2
Date solved : Monday, January 27, 2025 at 01:47:07 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+2 x y^{\prime }&=0 \end{align*}

Solution by Maple

Time used: 0.002 (sec). Leaf size: 10

dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)=0,y(x), singsol=all)
 
\[ y = c_1 +\operatorname {erf}\left (x \right ) c_2 \]

Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 21

DSolve[D[y[x],{x,2}]+2*x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \frac {1}{2} \sqrt {\pi } c_1 \text {erf}(x)+c_2 \]