Internal problem ID [5672]
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: 5 solved using series.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-x +y=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=8; dsolve([diff(y(x),x)=x-y(x),y(0) = 0],y(x),type='series',x=0);
\[ y \relax (x ) = \frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{120} x^{5}+\frac {1}{720} x^{6}-\frac {1}{5040} x^{7}+\mathrm {O}\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 46
AsymptoticDSolveValue[{y'[x]==x-y[x],{y[0]==0}},y[x],{x,0,7}]
\[ y(x)\to -\frac {x^7}{5040}+\frac {x^6}{720}-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2} \]