Internal problem ID [1316]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.5 THE METHOD OF FROBENIUS
I. Exercises 7.5. Page 358
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {6 x^{2} y^{\prime \prime }+x \left (10-x \right ) y^{\prime }-\left (2+x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 37
Order:=6; dsolve(6*x^2*diff(y(x),x$2)+x*(10-x)*diff(y(x),x)-(2+x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {4}{3}} \left (1+\frac {2}{21} x +\frac {1}{180} x^{2}+\frac {1}{4212} x^{3}+\frac {1}{124416} x^{4}+\frac {1}{4432320} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{1} \left (1+\mathrm {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 53
AsymptoticDSolveValue[6*x^2*y''[x]+x*(10-x)*y'[x]-(2+x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (\frac {x^5}{4432320}+\frac {x^4}{124416}+\frac {x^3}{4212}+\frac {x^2}{180}+\frac {2 x}{21}+1\right )+\frac {c_2}{x} \]