Internal problem ID [14814]
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: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}}=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 65
Order:=6; dsolve(diff(y(x),x$2)+(1/2*1/x-2)*diff(y(x),x)-35/16*1/x^2*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \frac {c_{1} x^{3} \left (1+\frac {7}{8} x +\frac {77}{160} x^{2}+\frac {77}{384} x^{3}+\frac {209}{3072} x^{4}+\frac {4807}{245760} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \left (x \right ) \left (\frac {15}{8} x^{3}+\frac {105}{64} x^{4}+\frac {231}{256} x^{5}+\operatorname {O}\left (x^{6}\right )\right )+\left (12+15 x +\frac {15}{4} x^{2}-\frac {13}{2} x^{3}-\frac {1741}{256} x^{4}-\frac {4141}{1024} x^{5}+\operatorname {O}\left (x^{6}\right )\right )\right )}{x^{\frac {5}{4}}} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 98
AsymptoticDSolveValue[y''[x]+(1/2*1/x-2)*y'[x]-35/16*1/x^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {209 x^{23/4}}{3072}+\frac {77 x^{19/4}}{384}+\frac {77 x^{15/4}}{160}+\frac {7 x^{11/4}}{8}+x^{7/4}\right )+c_1 \left (\frac {5}{256} x^{7/4} (7 x+8) \log (x)-\frac {627 x^4+608 x^3-320 x^2-1280 x-1024}{1024 x^{5/4}}\right ) \]