Internal problem ID [11755]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 20, Series solutions of second order linear equations. Exercises page
195
Problem number: 20.2 (iv) (k=-2).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-2 x y^{\prime }-4 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
Order:=6; dsolve(diff(y(x),x$2)-2*x*diff(y(x),x)-4*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1+2 x^{2}+\frac {4}{3} x^{4}\right ) y \left (0\right )+\left (x +x^{3}+\frac {1}{2} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[y''[x]-2*x*y'[x]-4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {x^5}{2}+x^3+x\right )+c_1 \left (\frac {4 x^4}{3}+2 x^2+1\right ) \]