Internal problem ID [6273]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 18. Power series solutions. Miscellaneous Exercises. page 394
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 50
Order:=8; dsolve(x*(1-2*x)*diff(y(x),x$2)-2*(2+x)*diff(y(x),x)+18*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{5} \left (1+\frac {16}{3} x +\frac {144}{7} x^{2}+\frac {480}{7} x^{3}+\frac {4400}{21} x^{4}+\frac {4224}{7} x^{5}+1664 x^{6}+\frac {13312}{3} x^{7}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (2880+12960 x +34560 x^{2}+57600 x^{3}-483840 x^{5}-2580480 x^{6}-9953280 x^{7}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.183 (sec). Leaf size: 81
AsymptoticDSolveValue[x*(1-2*x)*y''[x]-2*(2+x)*y'[x]+18*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (-896 x^6-168 x^5+20 x^3+12 x^2+\frac {9 x}{2}+1\right )+c_2 \left (1664 x^{11}+\frac {4224 x^{10}}{7}+\frac {4400 x^9}{21}+\frac {480 x^8}{7}+\frac {144 x^7}{7}+\frac {16 x^6}{3}+x^5\right ) \]