Internal problem ID [6141]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 25
Order:=8; dsolve((1+x^2)*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = y \relax (0)+D\relax (y )\relax (0) x -3 x^{2} y \relax (0)-\frac {D\relax (y )\relax (0) x^{3}}{3} \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 26
AsymptoticDSolveValue[(1+x^2)*y''[x]-4*x*y'[x]+6*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (x-\frac {x^3}{3}\right )+c_1 \left (1-3 x^2\right ) \]