Internal problem ID [6142]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+4\right ) y^{\prime \prime }+2 y^{\prime } x -12 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
Order:=8; dsolve((x^2+4)*diff(y(x),x$2)+2*x*diff(y(x),x)-12*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+\frac {3}{2} x^{2}+\frac {3}{16} x^{4}-\frac {1}{80} x^{6}\right ) y \left (0\right )+\left (x +\frac {5}{12} x^{3}\right ) D\left (y \right )\left (0\right )+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 42
AsymptoticDSolveValue[(x^2+4)*y''[x]+2*x*y'[x]-12*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_2 \left (\frac {5 x^3}{12}+x\right )+c_1 \left (-\frac {x^6}{80}+\frac {3 x^4}{16}+\frac {3 x^2}{2}+1\right ) \]