Internal problem ID [748]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1-x \right ) y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 26
Order:=6; dsolve((1-x)*diff(y(x),x)=y(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (x^{5}+x^{4}+x^{3}+x^{2}+x +1\right ) y \relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 21
AsymptoticDSolveValue[(1-x)*y'[x]==y[x],y[x],{x,0,5}]
\[ y(x)\to c_1 \left (x^5+x^4+x^3+x^2+x+1\right ) \]