78.17.2 problem 1 (b)

Internal problem ID [18408]
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 : 1 (b)
Date solved : Tuesday, January 28, 2025 at 11:49:34 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+y&=1 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 58

Order:=6; 
dsolve(diff(y(x),x)+y(x)=1,y(x),type='series',x=0);
 

\[ y = \left (1-x +\frac {1}{2} x^{2}-\frac {1}{6} x^{3}+\frac {1}{24} x^{4}-\frac {1}{120} x^{5}\right ) y \left (0\right )+x -\frac {x^{2}}{2}+\frac {x^{3}}{6}-\frac {x^{4}}{24}+\frac {x^{5}}{120}+O\left (x^{6}\right ) \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 69

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

\[ y(x)\to \frac {x^5}{120}-\frac {x^4}{24}+\frac {x^3}{6}-\frac {x^2}{2}+c_1 \left (-\frac {x^5}{120}+\frac {x^4}{24}-\frac {x^3}{6}+\frac {x^2}{2}-x+1\right )+x \]