Internal problem ID [1342]
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: 62.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {6 x^{2} \left (2 x^{2}+1\right ) y^{\prime \prime }+x \left (50 x^{2}+1\right ) y^{\prime }+\left (30 x^{2}+1\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: 35
Order:=6; dsolve(6*x^2*(1+2*x^2)*diff(y(x),x$2)+x*(1+50*x^2)*diff(y(x),x)+(1+30*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (4 x^{4}-2 x^{2}+1\right ) \left (\sqrt {x}\, c_{2}+x^{\frac {1}{3}} c_{1}\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 44
AsymptoticDSolveValue[6*x^2*(1+2*x^2)*y''[x]+x*(1+50*x^2)*y'[x]+(1+30*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt {x} \left (4 x^4-2 x^2+1\right )+c_2 \sqrt [3]{x} \left (4 x^4-2 x^2+1\right ) \]