73.23.11 problem 33.3 (k)

Internal problem ID [15657]
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 (k)
Date solved : Tuesday, January 28, 2025 at 08:03:45 AM
CAS classification : [_separable]

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

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 34

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

\[ y = \left (1+\frac {1}{2} x^{2}-\frac {1}{3} x^{3}+\frac {3}{8} x^{4}-\frac {11}{30} x^{5}\right ) y \left (0\right )+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 36

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

\[ y(x)\to c_1 \left (-\frac {11 x^5}{30}+\frac {3 x^4}{8}-\frac {x^3}{3}+\frac {x^2}{2}+1\right ) \]