Internal problem ID [6489]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\left (x -6\right ) 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: 47
Order:=6; dsolve(diff(y(x), x, x) + (x-6)*y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+3 x^{2}-\frac {1}{6} x^{3}+\frac {3}{2} x^{4}-\frac {1}{5} x^{5}\right ) y \relax (0)+\left (x +x^{3}-\frac {1}{12} x^{4}+\frac {3}{10} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 57
AsymptoticDSolveValue[y''[x]+(x-6)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {3 x^5}{10}-\frac {x^4}{12}+x^3+x\right )+c_1 \left (-\frac {x^5}{5}+\frac {3 x^4}{2}-\frac {x^3}{6}+3 x^2+1\right ) \]