Internal problem ID [6482]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x -2\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1+x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.021 (sec). Leaf size: 42
Order:=6; dsolve((x-2)*diff(y(x), x$2) + 1/x*diff(y(x), x) + (x+1)*y(x) = 0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{\frac {3}{2}} \left (1+\frac {3}{20} x +\frac {25}{224} x^{2}+\frac {1361}{17280} x^{3}+\frac {80753}{2365440} x^{4}+\frac {616517}{38707200} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1+\frac {1}{2} x^{2}+\frac {2}{9} x^{3}+\frac {11}{120} x^{4}+\frac {82}{1575} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 80
AsymptoticDSolveValue[(x-2)*y''[x] + 1/x*y'[x] + (x+1)*y[x] ==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {82 x^5}{1575}+\frac {11 x^4}{120}+\frac {2 x^3}{9}+\frac {x^2}{2}+1\right )+c_1 \left (\frac {616517 x^5}{38707200}+\frac {80753 x^4}{2365440}+\frac {1361 x^3}{17280}+\frac {25 x^2}{224}+\frac {3 x}{20}+1\right ) x^{3/2} \]