Internal problem ID [14812]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 35
Order:=6; dsolve(diff(y(x),x$2)+8/3*1/x*diff(y(x),x)-(2/3*1/x^2-1)*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{2} x^{\frac {7}{3}} \left (1-\frac {3}{26} x^{2}+\frac {9}{1976} x^{4}+\operatorname {O}\left (x^{6}\right )\right )+c_{1} \left (1+\frac {3}{2} x^{2}-\frac {9}{40} x^{4}+\operatorname {O}\left (x^{6}\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 50
AsymptoticDSolveValue[y''[x]+8/3*1/x*y'[x]-(2/3*1/x^2-1)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (\frac {9 x^4}{1976}-\frac {3 x^2}{26}+1\right )+\frac {c_2 \left (-\frac {9 x^4}{40}+\frac {3 x^2}{2}+1\right )}{x^2} \]