Internal problem ID [14780]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }-18 y=0} \] 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)+3*diff(y(x),x)-18*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+9 x^{2}-9 x^{3}+\frac {81}{4} x^{4}-\frac {81}{4} x^{5}\right ) y \left (0\right )+\left (x -\frac {3}{2} x^{2}+\frac {9}{2} x^{3}-\frac {45}{8} x^{4}+\frac {297}{40} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 66
AsymptoticDSolveValue[y''[x]+3*y'[x]-18*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {81 x^5}{4}+\frac {81 x^4}{4}-9 x^3+9 x^2+1\right )+c_2 \left (\frac {297 x^5}{40}-\frac {45 x^4}{8}+\frac {9 x^3}{2}-\frac {3 x^2}{2}+x\right ) \]