Internal problem ID [1366]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.6 THE METHOD OF FROBENIUS
II. Exercises 7.6. Page 374
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (x +1\right ) y^{\prime \prime }-x \left (-x +3\right ) y^{\prime }+4 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: 69
Order:=6; dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(3-x)*diff(y(x),x)+4*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = x^{2} \left (\left (c_{2} \ln \relax (x )+c_{1}\right ) \left (1-4 x +9 x^{2}-16 x^{3}+25 x^{4}-36 x^{5}+\mathrm {O}\left (x^{6}\right )\right )+\left (4 x -12 x^{2}+24 x^{3}-40 x^{4}+60 x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 98
AsymptoticDSolveValue[x^2*(1+x)*y''[x]-x*(3-x)*y'[x]+4*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-36 x^5+25 x^4-16 x^3+9 x^2-4 x+1\right ) x^2+c_2 \left (\left (60 x^5-40 x^4+24 x^3-12 x^2+4 x\right ) x^2+\left (-36 x^5+25 x^4-16 x^3+9 x^2-4 x+1\right ) x^2 \log (x)\right ) \]