Internal problem ID [14805]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 54
Order:=6; dsolve((x^2-25)^2*diff(y(x),x$2)-(x+5)*diff(y(x),x)+10*y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (1-\frac {1}{125} x^{2}-\frac {1}{46875} x^{3}-\frac {767}{7812500} x^{4}-\frac {4813}{7324218750} x^{5}\right ) y \left (0\right )+\left (x +\frac {1}{250} x^{2}-\frac {112}{46875} x^{3}+\frac {173}{3906250} x^{4}-\frac {409681}{7324218750} x^{5}\right ) D\left (y \right )\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 70
AsymptoticDSolveValue[(x^2-25)^2*y''[x]-(x+5)*y'[x]+10*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {4813 x^5}{7324218750}-\frac {767 x^4}{7812500}-\frac {x^3}{46875}-\frac {x^2}{125}+1\right )+c_2 \left (-\frac {409681 x^5}{7324218750}+\frac {173 x^4}{3906250}-\frac {112 x^3}{46875}+\frac {x^2}{250}+x\right ) \]