Internal problem ID [6224]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 18. Power series solutions. 18.8 Indicial Equation with Difference of Roots a
Positive Integer: Nonlogarithmic Case. Exercises page 380
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.037 (sec). Leaf size: 52
Order:=8; dsolve(x*(x+3)*diff(y(x),x$2)-9*diff(y(x),x)-6*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{4} \left (1-\frac {2}{5} x +\frac {7}{45} x^{2}-\frac {8}{135} x^{3}+\frac {1}{45} x^{4}-\frac {2}{243} x^{5}+\frac {11}{3645} x^{6}-\frac {4}{3645} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (-144+96 x -48 x^{2}+\frac {64}{3} x^{3}-\frac {80}{9} x^{4}+\frac {32}{9} x^{5}-\frac {112}{81} x^{6}+\frac {128}{243} x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.35 (sec). Leaf size: 98
AsymptoticDSolveValue[x*(x+3)*y''[x]-9*y'[x]-6*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {7 x^6}{729}-\frac {2 x^5}{81}+\frac {5 x^4}{81}-\frac {4 x^3}{27}+\frac {x^2}{3}-\frac {2 x}{3}+1\right )+c_2 \left (\frac {11 x^{10}}{3645}-\frac {2 x^9}{243}+\frac {x^8}{45}-\frac {8 x^7}{135}+\frac {7 x^6}{45}-\frac {2 x^5}{5}+x^4\right ) \]