1.1 problem 1. Using series method

Internal problem ID [5791]

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]]

Solve \begin {gather*} \boxed {y^{\prime }-y^{2}+x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}

With the expansion point for the power series method at \(x = 0\).

Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

Order:=8; 
dsolve([diff(y(x),x)=y(x)^2-x,y(0) = 1],y(x),type='series',x=0);
 

\[ y \relax (x ) = 1+x +\frac {1}{2} x^{2}+\frac {2}{3} x^{3}+\frac {7}{12} x^{4}+\frac {11}{20} x^{5}+\frac {22}{45} x^{6}+\frac {559}{1260} x^{7}+\mathrm {O}\left (x^{8}\right ) \]

Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 48

AsymptoticDSolveValue[{y'[x]==y[x]^2-x,{y[0]==1}},y[x],{x,0,7}]
 

\[ y(x)\to \frac {559 x^7}{1260}+\frac {22 x^6}{45}+\frac {11 x^5}{20}+\frac {7 x^4}{12}+\frac {2 x^3}{3}+\frac {x^2}{2}+x+1 \]