Internal problem ID [4882]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (x -2\right ) y^{\prime }-x y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (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);
\[ y \relax (x ) = 4-x^{2}-\frac {1}{3} x^{3}+\frac {1}{30} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 24
AsymptoticDSolveValue[{(x-2)*y'[x]==x*y[x],{y[0]==4}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{30}-\frac {x^3}{3}-x^2+4 \]