Internal problem ID [399]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Chapter 11 Power series methods. Section 11.1 Introduction and Review of power series. Page
615
Problem number: problem 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {2 \left (x +1\right ) y^{\prime }-y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
Order:=6; dsolve(2*(x+1)*diff(y(x),x)=y(x),y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {1}{2} x -\frac {1}{8} x^{2}+\frac {1}{16} x^{3}-\frac {5}{128} x^{4}+\frac {7}{256} x^{5}\right ) y \relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 41
AsymptoticDSolveValue[2*(x+1)*y'[x]==y[x],y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {7 x^5}{256}-\frac {5 x^4}{128}+\frac {x^3}{16}-\frac {x^2}{8}+\frac {x}{2}+1\right ) \]