7.13.16 problem 16

Internal problem ID [415]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 3. Power series methods. Section 3.1 (Introduction). Problems at page 206
Problem number : 16
Date solved : Monday, January 27, 2025 at 02:53:30 AM
CAS classification : [_separable]

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

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 14

Order:=6; 
dsolve(2*x*diff(y(x),x)=y(x),y(x),type='series',x=0);
 

\[ y = c_1 \sqrt {x}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 11

AsymptoticDSolveValue[2*x*D[y[x],x]==y[x],y[x],{x,0,"6"-1}]
 

\[ y(x)\to c_1 \sqrt {x} \]