Internal problem ID [6155]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th edition.
1997.
Section: CHAPTER 17. Power series solutions. 17.5. Solutions Near an Ordinary Point. Exercises page
355
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 y^{\prime \prime }+9 x y^{\prime }-36 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 39
Order:=8; dsolve(2*diff(y(x),x$2)+9*x*diff(y(x),x)-36*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\frac {27}{4} x^{4}+9 x^{2}+1\right ) y \relax (0)+\left (x +\frac {9}{4} x^{3}+\frac {81}{160} x^{5}-\frac {243}{4480} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 47
AsymptoticDSolveValue[2*y''[x]+9*x*y'[x]-36*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {27 x^4}{4}+9 x^2+1\right )+c_2 \left (-\frac {243 x^7}{4480}+\frac {81 x^5}{160}+\frac {9 x^3}{4}+x\right ) \]