Internal problem ID [6257]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_erf]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 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: 0.0 (sec). Leaf size: 37
Order:=8; dsolve(diff(y(x),x$2)+2*x*diff(y(x),x)-8*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\frac {4}{3} x^{4}+4 x^{2}+1\right ) y \relax (0)+\left (x +x^{3}+\frac {1}{10} x^{5}-\frac {1}{210} x^{7}\right ) D\relax (y )\relax (0)+O\left (x^{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 43
AsymptoticDSolveValue[y''[x]+2*x*y'[x]-8*y[x]==0,y[x],{x,0,7}]
\[ y(x)\to c_1 \left (\frac {4 x^4}{3}+4 x^2+1\right )+c_2 \left (-\frac {x^7}{210}+\frac {x^5}{10}+x^3+x\right ) \]