Internal problem ID [1434]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.6 THE METHOD OF FROBENIUS
III. Exercises 7.7. Page 389
Problem number: 18.
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 }+3 y^{\prime } x^{2}-\left (6-x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 39
Order:=6; dsolve(x^2*(1+x)*diff(y(x),x$2)+3*x^2*diff(y(x),x)-(6-x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{3} \left (1-\frac {8}{3} x +\frac {100}{21} x^{2}-\frac {50}{7} x^{3}+\frac {175}{18} x^{4}-\frac {112}{9} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\frac {c_{2} \left (2880+720 x +\mathrm {O}\left (x^{6}\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 53
AsymptoticDSolveValue[x^2*(1+x)*y''[x]+3*x^2*y'[x]-(6-x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^2}+\frac {1}{4 x}\right )+c_2 \left (\frac {175 x^7}{18}-\frac {50 x^6}{7}+\frac {100 x^5}{21}-\frac {8 x^4}{3}+x^3\right ) \]