78.17.6 problem 5

Internal problem ID [18412]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 5. Power Series Solutions and Special Functions. Section 27. Series Solutions of First Order Equations. Problems at page 208
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 11:49:36 AM
CAS classification : [[_linear, `class A`]]

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

Using series method with expansion around

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

Order:=6; 
dsolve([diff(y(x),x)=x-y(x),y(0) = 0],y(x),type='series',x=0);
 

\[ y = \frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{120} x^{5}+\operatorname {O}\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 32

AsymptoticDSolveValue[{D[y[x],x]==x-y[x],{y[0]==0}},y[x],{x,0,"6"-1}]
 

\[ y(x)\to -\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2} \]