10.14.16 problem 19

Internal problem ID [1398]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 5.3, Series Solutions Near an Ordinary Point, Part II. page 269
Problem number : 19
Date solved : Monday, January 27, 2025 at 04:56:44 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 21

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

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