29.7.5 problem 2

Internal problem ID [7322]
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 : Tuesday, September 30, 2025 at 04:28:52 PM
CAS classification : [[_2nd_order, _missing_y]]

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

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

ode:=diff(diff(y(x),x),x)+2*x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +\operatorname {erf}\left (x \right ) c_2 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to \frac {1}{2} \sqrt {\pi } c_1 \text {erf}(x)+c_2 \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \operatorname {erf}{\left (x \right )} \]