Internal problem ID [5653]
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(b) solving using series.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }+y-1=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: 60
Order:=8; dsolve(diff(y(x),x)+y(x)=1,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-x +\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{120} x^{5}+\frac {1}{720} x^{6}-\frac {1}{5040} x^{7}\right ) y \relax (0)+x -\frac {x^{2}}{2}+\frac {x^{3}}{6}-\frac {x^{4}}{24}+\frac {x^{5}}{120}-\frac {x^{6}}{720}+\frac {x^{7}}{5040}+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 97
AsymptoticDSolveValue[y'[x]+y[x]==1,y[x],{x,0,7}]
\[ y(x)\to \frac {x^7}{5040}-\frac {x^6}{720}+\frac {x^5}{120}-\frac {x^4}{24}+\frac {x^3}{6}-\frac {x^2}{2}+c_1 \left (-\frac {x^7}{5040}+\frac {x^6}{720}-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right )+x \]