Internal problem ID [1299]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {12 x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (3 x^{2}+35 x +11\right ) y^{\prime }-\left (-5 x^{2}-10 x +1\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 47
Order:=6; dsolve(12*x^2*(1+x)*diff(y(x),x$2)+x*(11+35*x+3*x^2)*diff(y(x),x)-(1-10*x-5*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {7}{12}} \left (1-x +\frac {28}{31} x^{2}-\frac {1111}{1333} x^{3}+\frac {57493}{73315} x^{4}-\frac {3668716}{4912105} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{1} \left (1-x +\frac {7}{8} x^{2}-\frac {19}{24} x^{3}+\frac {283}{384} x^{4}-\frac {1339}{1920} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x^{\frac {1}{4}}} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 86
AsymptoticDSolveValue[12*x^2*(1+x)*y''[x]+x*(11+35*x+3*x^2)*y'[x]-(1-10*x-5*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (-\frac {3668716 x^5}{4912105}+\frac {57493 x^4}{73315}-\frac {1111 x^3}{1333}+\frac {28 x^2}{31}-x+1\right )+\frac {c_2 \left (-\frac {1339 x^5}{1920}+\frac {283 x^4}{384}-\frac {19 x^3}{24}+\frac {7 x^2}{8}-x+1\right )}{\sqrt [4]{x}} \]