Internal problem ID [1348]
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: 68.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} \left (x^{2}+2 x +3\right ) y^{\prime \prime }-x \left (-15 x^{2}-14 x +3\right ) y^{\prime }+\left (7 x^{2}+3\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: 45
Order:=6; dsolve(4*x^2*(3+2*x+x^2)*diff(y(x),x$2)-x*(3-14*x-15*x^2)*diff(y(x),x)+(3+7*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {2}{3} x +\frac {1}{9} x^{2}+\frac {4}{27} x^{3}-\frac {11}{81} x^{4}+\frac {10}{243} x^{5}\right ) \left (x^{\frac {1}{4}} c_{1}+c_{2} x \right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 86
AsymptoticDSolveValue[4*x^2*(3+2*x+x^2)*y''[x]-x*(3-14*x-15*x^2)*y'[x]+(3+7*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x \left (\frac {10 x^5}{243}-\frac {11 x^4}{81}+\frac {4 x^3}{27}+\frac {x^2}{9}-\frac {2 x}{3}+1\right )+c_2 \sqrt [4]{x} \left (\frac {10 x^5}{243}-\frac {11 x^4}{81}+\frac {4 x^3}{27}+\frac {x^2}{9}-\frac {2 x}{3}+1\right ) \]