Internal problem ID [14815]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.9, page 215
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 63
Order:=6; dsolve(diff(y(x),x$2)-(1/x+2)*diff(y(x),x)+(x+1/x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (\left (c_{1} +c_{2} \ln \left (x \right )\right ) \left (1+2 x +2 x^{2}+\frac {11}{9} x^{3}+\frac {35}{72} x^{4}+\frac {103}{900} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (\left (-2\right ) x -3 x^{2}-\frac {64}{27} x^{3}-\frac {497}{432} x^{4}-\frac {9371}{27000} x^{5}+\operatorname {O}\left (x^{6}\right )\right ) c_{2} \right ) x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 110
AsymptoticDSolveValue[y''[x]-(1/x+2)*y'[x]+(x+1/x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x \left (\frac {103 x^5}{900}+\frac {35 x^4}{72}+\frac {11 x^3}{9}+2 x^2+2 x+1\right )+c_2 \left (x \left (-\frac {9371 x^5}{27000}-\frac {497 x^4}{432}-\frac {64 x^3}{27}-3 x^2-2 x\right )+x \left (\frac {103 x^5}{900}+\frac {35 x^4}{72}+\frac {11 x^3}{9}+2 x^2+2 x+1\right ) \log (x)\right ) \]