73.23.12 problem 33.3 (L)

Internal problem ID [15658]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 33. Power series solutions I: Basic computational methods. Additional Exercises. page 641
Problem number : 33.3 (L)
Date solved : Tuesday, January 28, 2025 at 08:03:45 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

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

\[ y = \left (1-x +\frac {3}{2} x^{2}-\frac {11}{6} x^{3}+\frac {53}{24} x^{4}-\frac {103}{40} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 39

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

\[ y(x)\to c_1 \left (-\frac {103 x^5}{40}+\frac {53 x^4}{24}-\frac {11 x^3}{6}+\frac {3 x^2}{2}-x+1\right ) \]