Internal problem ID [1201]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.1 Exercises. Page 318
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x^{2}-6 x +1\right ) y^{\prime }+\left (x^{2}+6 x +1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 63
Order:=6; dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(1-6*x-x^2)*diff(y(x),x)+(1+6*x+x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\left (c_{2} \ln \relax (x )+c_{1}\right ) \left (1-12 x +\frac {119}{2} x^{2}-\frac {583}{3} x^{3}+\frac {1981}{4} x^{4}-\frac {80287}{75} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (17 x -\frac {471}{4} x^{2}+445 x^{3}-\frac {118285}{96} x^{4}+\frac {702451}{250} x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 114
AsymptoticDSolveValue[x^2*(1+x)*y''[x]-x*(1-6*x-x^2)*y'[x]+(1+6*x+x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x \left (-\frac {80287 x^5}{75}+\frac {1981 x^4}{4}-\frac {583 x^3}{3}+\frac {119 x^2}{2}-12 x+1\right )+c_2 \left (x \left (\frac {702451 x^5}{250}-\frac {118285 x^4}{96}+445 x^3-\frac {471 x^2}{4}+17 x\right )+x \left (-\frac {80287 x^5}{75}+\frac {1981 x^4}{4}-\frac {583 x^3}{3}+\frac {119 x^2}{2}-12 x+1\right ) \log (x)\right ) \]