Internal problem ID [1367]
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
II. Exercises 7.6. Page 374
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1-2 x \right ) y^{\prime \prime }-x \left (5-4 x \right ) y^{\prime }+\left (9-4 x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 69
Order:=6; dsolve(x^2*(1-2*x)*diff(y(x),x$2)-x*(5-4*x)*diff(y(x),x)+(9-4*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1+4 x +12 x^{2}+32 x^{3}+80 x^{4}+192 x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (\left (-2\right ) x -8 x^{2}-24 x^{3}-64 x^{4}-160 x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) x^{3} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 98
AsymptoticDSolveValue[x^2*(1-2*x)*y''[x]-x*(5-4*x)*y'[x]+(9-4*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (192 x^5+80 x^4+32 x^3+12 x^2+4 x+1\right ) x^3+c_2 \left (\left (-160 x^5-64 x^4-24 x^3-8 x^2-2 x\right ) x^3+\left (192 x^5+80 x^4+32 x^3+12 x^2+4 x+1\right ) x^3 \log (x)\right ) \]