Internal problem ID [6258]
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: 9.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
Solve \begin {gather*} \boxed {x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 32
Order:=8; dsolve(x*(1-x^2)*diff(y(x),x$2)-(7+x^2)*diff(y(x),x)+4*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{8} \left (1+3 x^{2}+6 x^{4}+10 x^{6}+\mathrm {O}\left (x^{8}\right )\right )+c_{2} \left (-203212800-67737600 x^{2}+\mathrm {O}\left (x^{8}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 38
AsymptoticDSolveValue[x*(1-x^2)*y''[x]-(7+x^2)*y'[x]+4*x*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {x^2}{3}+1\right )+c_2 \left (10 x^{14}+6 x^{12}+3 x^{10}+x^8\right ) \]