Internal problem ID [4708]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 27. Power series solutions of linear DE with variable coefficients. Supplementary
Problems. page 274
Problem number: Problem 27.28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 49
Order:=6; dsolve((x+1)*diff(y(x),x$2)+1/x*diff(y(x),x)+x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1-\frac {1}{9} x^{3}+\frac {1}{24} x^{4}-\frac {1}{50} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (x +\frac {2}{27} x^{3}-\frac {11}{144} x^{4}+\frac {33}{1000} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 82
AsymptoticDSolveValue[(1+x)*y''[x]+1/x*y'[x]+x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {x^5}{50}+\frac {x^4}{24}-\frac {x^3}{9}+1\right )+c_2 \left (\frac {33 x^5}{1000}-\frac {11 x^4}{144}+\frac {2 x^3}{27}+\left (-\frac {x^5}{50}+\frac {x^4}{24}-\frac {x^3}{9}+1\right ) \log (x)+x\right ) \]