Internal problem ID [6157]
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: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x^{2}+4\right ) y^{\prime \prime }+3 x y^{\prime }-8 y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 32
Order:=8; dsolve((x^2+4)*diff(y(x),x$2)+3*x*diff(y(x),x)-8*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (x^{2}+1\right ) y \relax (0)+\left (x +\frac {5}{24} x^{3}-\frac {7}{384} x^{5}+\frac {3}{1024} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 38
AsymptoticDSolveValue[(x^2+4)*y''[x]+3*x*y'[x]-8*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (x^2+1\right )+c_2 \left (\frac {3 x^7}{1024}-\frac {7 x^5}{384}+\frac {5 x^3}{24}+x\right ) \]