Internal problem ID [14781]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-11 y^{\prime }+30 y=0} \] 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)-11*diff(y(x),x)+30*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-15 x^{2}-55 x^{3}-\frac {455}{4} x^{4}-\frac {671}{4} x^{5}\right ) y \left (0\right )+\left (x +\frac {11}{2} x^{2}+\frac {91}{6} x^{3}+\frac {671}{24} x^{4}+\frac {4651}{120} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 66
AsymptoticDSolveValue[y''[x]-11*y'[x]+30*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {671 x^5}{4}-\frac {455 x^4}{4}-55 x^3-15 x^2+1\right )+c_2 \left (\frac {4651 x^5}{120}+\frac {671 x^4}{24}+\frac {91 x^3}{6}+\frac {11 x^2}{2}+x\right ) \]