Internal problem ID [1345]
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: 65.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {8 x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+2 x \left (-21 x^{2}+10\right ) y^{\prime }-\left (35 x^{2}+2\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
Order:=6; dsolve(8*x^2*(2-x^2)*diff(y(x),x$2)+2*x*(10-21*x^2)*diff(y(x),x)-(2+35*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {\left (1+\frac {1}{2} x^{2}+\frac {1}{4} x^{4}\right ) \left (x^{\frac {3}{4}} c_{2}+c_{1}\right )}{\sqrt {x}}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 52
AsymptoticDSolveValue[8*x^2*(2-x^2)*y''[x]+2*x*(10-21*x^2)*y'[x]-(2+35*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [4]{x} \left (\frac {x^4}{4}+\frac {x^2}{2}+1\right )+\frac {c_2 \left (\frac {x^4}{4}+\frac {x^2}{2}+1\right )}{\sqrt {x}} \]