46.1.13 problem 19

Internal problem ID [7303]
Book : ADVANCED ENGINEERING MATHEMATICS. ERWIN KREYSZIG, HERBERT KREYSZIG, EDWARD J. NORMINTON. 10th edition. John Wiley USA. 2011
Section : Chapter 5. Series Solutions of ODEs. Special Functions. Problem set 5.1. page 174
Problem number : 19
Date solved : Monday, January 27, 2025 at 02:49:58 PM
CAS classification : [_separable]

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

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

Order:=6; 
dsolve([(x-2)*diff(y(x),x)=x*y(x),y(0) = 4],y(x),type='series',x=0);
 

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

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 24

AsymptoticDSolveValue[{(x-2)*D[y[x],x]==x*y[x],{y[0]==4}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to \frac {x^5}{30}-\frac {x^3}{3}-x^2+4 \]