Internal problem ID [6556]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
Order:=8; dsolve(diff(y(x),x$2)+2*diff(y(x),x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = y \left (0\right )+\left (x -x^{2}+\frac {2}{3} x^{3}-\frac {1}{3} x^{4}+\frac {2}{15} x^{5}-\frac {2}{45} x^{6}+\frac {4}{315} x^{7}\right ) D\left (y \right )\left (0\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 51
AsymptoticDSolveValue[y''[x]+2*y'[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {4 x^7}{315}-\frac {2 x^6}{45}+\frac {2 x^5}{15}-\frac {x^4}{3}+\frac {2 x^3}{3}-x^2+x\right )+c_1 \]