Internal problem ID [6544]
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: 1. Using series method.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_Riccati, _special]]
\[ \boxed {-y^{2}+y^{\prime }=-x} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
Order:=8; dsolve([diff(y(x),x)=y(x)^2-x,y(0) = 1],y(x),type='series',x=0);
\[ y \left (x \right ) = 1+x +\frac {1}{2} x^{2}+\frac {2}{3} x^{3}+\frac {7}{12} x^{4}+\frac {11}{20} x^{5}+\frac {22}{45} x^{6}+\frac {559}{1260} x^{7}+\operatorname {O}\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 48
AsymptoticDSolveValue[{y'[x]==y[x]^2-x,{y[0]==1}},y[x],{x,0,7}]
\[ y(x)\to \frac {559 x^7}{1260}+\frac {22 x^6}{45}+\frac {11 x^5}{20}+\frac {7 x^4}{12}+\frac {2 x^3}{3}+\frac {x^2}{2}+x+1 \]