51.1.1 problem 1. Using series method

Internal problem ID [8212]
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
Date solved : Monday, January 27, 2025 at 03:46:04 PM
CAS classification : [[_Riccati, _special]]

\begin{align*} y^{\prime }&=y^{2}-x \end{align*}

Using series method with expansion around

\begin{align*} 0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 7.979 (sec). Leaf size: 1113

AsymptoticDSolveValue[{D[y[x],x]==y[x]^2-x,{y[0]==1}},y[x],{x,0,"8"-1}]
 

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