7.13.7 problem 7

Internal problem ID [406]
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 : 7
Date solved : Monday, January 27, 2025 at 02:53:26 AM
CAS classification : [_separable]

\begin{align*} \left (2 x -1\right ) y^{\prime }+2 y&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 37

Order:=6; 
dsolve((2*x-1)*diff(y(x),x)+2*y(x)=0,y(x),type='series',x=0);
 

\[ y = \left (32 x^{5}+16 x^{4}+8 x^{3}+4 x^{2}+2 x +1\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 31

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

\[ y(x)\to c_1 \left (32 x^5+16 x^4+8 x^3+4 x^2+2 x+1\right ) \]