Internal problem ID [5793]
Book: A course in Ordinary Differential Equations. by Stephen A. Wirkus, Randall J. Swift. CRC
Press NY. 2015. 2nd Edition
Section: Chapter 8. Series Methods. section 8.2. The Power Series Method. Problems Page
603
Problem number: 2. Using series method.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {-2 y+y^{\prime }-x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
With the expansion point for the power series method at \(x = 1\).
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 24
Order:=8; dsolve([diff(y(x),x)-2*y(x)=x^2,y(1) = 1],y(x),type='series',x=1);
\[ y \relax (x ) = 1+3 \left (x -1\right )+4 \left (x -1\right )^{2}+3 \left (x -1\right )^{3}+\frac {3}{2} \left (x -1\right )^{4}+\frac {3}{5} \left (x -1\right )^{5}+\frac {1}{5} \left (x -1\right )^{6}+\frac {2}{35} \left (x -1\right )^{7}+\mathrm {O}\left (\left (x -1\right )^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 60
AsymptoticDSolveValue[{y'[x]-2*y[x]==x^2,{y[1]==1}},y[x],{x,1,7}]
\[ y(x)\to \frac {2}{35} (x-1)^7+\frac {1}{5} (x-1)^6+\frac {3}{5} (x-1)^5+\frac {3}{2} (x-1)^4+3 (x-1)^3+4 (x-1)^2+3 (x-1)+1 \]