Internal problem ID [1298]
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: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }+x \left (4 x^{2}+2 x +7\right ) y^{\prime }-\left (-7 x^{2}-4 x +1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 47
Order:=6; dsolve(4*x^2*diff(y(x),x$2)+x*(7+2*x+4*x^2)*diff(y(x),x)-(1-4*x-7*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {5}{4}} \left (1-\frac {1}{2} x -\frac {19}{104} x^{2}+\frac {1571}{10608} x^{3}+\frac {3225}{198016} x^{4}-\frac {752183}{29702400} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{1} \left (1+2 x -\frac {11}{6} x^{2}-\frac {1}{7} x^{3}+\frac {895}{1848} x^{4}-\frac {499}{13860} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 86
AsymptoticDSolveValue[4*x^2*y''[x]+x*(7+2*x+4*x^2)*y'[x]-(1-4*x-7*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [4]{x} \left (-\frac {752183 x^5}{29702400}+\frac {3225 x^4}{198016}+\frac {1571 x^3}{10608}-\frac {19 x^2}{104}-\frac {x}{2}+1\right )+\frac {c_2 \left (-\frac {499 x^5}{13860}+\frac {895 x^4}{1848}-\frac {x^3}{7}-\frac {11 x^2}{6}+2 x+1\right )}{x} \]