36.6.7 problem 7

Internal problem ID [6368]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number : 7
Date solved : Monday, January 27, 2025 at 01:58:18 PM
CAS classification : [_separable]

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

Using series method with expansion around

\begin{align*} 1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

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

\[ y = \left (1-\left (x -1\right )^{2}+\frac {\left (x -1\right )^{4}}{2}\right ) y \left (1\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 24

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

\[ y(x)\to c_1 \left (\frac {1}{2} (x-1)^4-(x-1)^2+1\right ) \]