Internal problem ID [5655]
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(c) solving using series.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-y-2=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 58
Order:=8; dsolve(diff(y(x),x)-y(x)=2,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+x +\frac {1}{2} x^{2}+\frac {1}{6} x^{3}+\frac {1}{24} x^{4}+\frac {1}{120} x^{5}+\frac {1}{720} x^{6}+\frac {1}{5040} x^{7}\right ) y \relax (0)+2 x +x^{2}+\frac {x^{3}}{3}+\frac {x^{4}}{12}+\frac {x^{5}}{60}+\frac {x^{6}}{360}+\frac {x^{7}}{2520}+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 93
AsymptoticDSolveValue[y'[x]-y[x]==2,y[x],{x,0,7}]
\[ y(x)\to \frac {x^7}{2520}+\frac {x^6}{360}+\frac {x^5}{60}+\frac {x^4}{12}+\frac {x^3}{3}+x^2+c_1 \left (\frac {x^7}{5040}+\frac {x^6}{720}+\frac {x^5}{120}+\frac {x^4}{24}+\frac {x^3}{6}+\frac {x^2}{2}+x+1\right )+2 x \]