Internal problem ID [1343]
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: 63.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {28 x^{2} \left (-3 x +1\right ) y^{\prime \prime }-7 x \left (5+9 x \right ) y^{\prime }+7 \left (2+9 x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 47
Order:=6; dsolve(28*x^2*(1-3*x)*diff(y(x),x$2)-7*x*(5+9*x)*diff(y(x),x)+7*(2+9*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (243 x^{5}+81 x^{4}+27 x^{3}+9 x^{2}+3 x +1\right ) \left (x^{2} c_{2}+x^{\frac {1}{4}} c_{1}\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 68
AsymptoticDSolveValue[28*x^2*(1-3*x)*y''[x]-7*x*(5+9*x)*y'[x]+7*(2+9*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (243 x^5+81 x^4+27 x^3+9 x^2+3 x+1\right ) x^2+c_2 \left (243 x^5+81 x^4+27 x^3+9 x^2+3 x+1\right ) \sqrt [4]{x} \]