Internal problem ID [14884]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 63.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
Order:=6; dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-2 x^{2}-\frac {8}{3} x^{3}-2 x^{4}-\frac {16}{15} x^{5}\right ) y \left (0\right )+\left (x +2 x^{2}+2 x^{3}+\frac {4}{3} x^{4}+\frac {2}{3} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 62
AsymptoticDSolveValue[y''[x]-4*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {16 x^5}{15}-2 x^4-\frac {8 x^3}{3}-2 x^2+1\right )+c_2 \left (\frac {2 x^5}{3}+\frac {4 x^4}{3}+2 x^3+2 x^2+x\right ) \]