Internal problem ID [4806]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.2 page
239
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (x -1\right )^{3}}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 52
Order:=6; dsolve(diff(y(x),x$2)-1/x*diff(y(x),x)+1/(x-1)^3*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{2} \left (1+\frac {1}{8} x^{2}+\frac {1}{5} x^{3}+\frac {49}{192} x^{4}+\frac {423}{1400} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (-x^{2}-\frac {1}{8} x^{4}-\frac {1}{5} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (-2-2 x^{3}-\frac {45}{32} x^{4}-\frac {34}{25} x^{5}+\mathrm {O}\left (x^{6}\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 71
AsymptoticDSolveValue[y''[x]-1/x*y'[x]+1/(x-1)^3*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{16} \left (x^2+8\right ) x^2 \log (x)+\frac {1}{64} \left (-5 x^4+64 x^3-400 x^2+64\right )\right )+c_2 \left (\frac {49 x^6}{192}+\frac {x^5}{5}+\frac {x^4}{8}+x^2\right ) \]