52.1.7 problem 6. series method

Internal problem ID [8224]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. Section 6.2 SOLUTIONS ABOUT ORDINARY POINTS. EXERCISES 6.2. Page 246
Problem number : 6. series method
Date solved : Monday, January 27, 2025 at 03:46:24 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }&=0 \end{align*}

Using series method with expansion around

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 46

Order:=8; 
dsolve(diff(y(x),x$2)+2*diff(y(x),x)=0,y(x),type='series',x=0);
 

\[ y = y \left (0\right )+\left (x -x^{2}+\frac {2}{3} x^{3}-\frac {1}{3} x^{4}+\frac {2}{15} x^{5}-\frac {2}{45} x^{6}+\frac {4}{315} x^{7}\right ) y^{\prime }\left (0\right )+O\left (x^{8}\right ) \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 51

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

\[ y(x)\to c_2 \left (\frac {4 x^7}{315}-\frac {2 x^6}{45}+\frac {2 x^5}{15}-\frac {x^4}{3}+\frac {2 x^3}{3}-x^2+x\right )+c_1 \]