Internal problem ID [6410]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of
First-Order Differential Equations Page 162
Problem number: 1(d) solving using series.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y+y^{\prime }=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 46
Order:=8; dsolve(diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-x +\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{120} x^{5}+\frac {1}{720} x^{6}-\frac {1}{5040} x^{7}\right ) y \left (0\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 53
AsymptoticDSolveValue[y'[x]+y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (-\frac {x^7}{5040}+\frac {x^6}{720}-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right ) \]