Internal problem ID [1310]
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: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} y^{\prime \prime }+9 y^{\prime } x -\left (3 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(9*x^2*diff(y(x),x$2)+9*x*diff(y(x),x)-(1+3*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {2}{3}} \left (1+\frac {1}{5} x +\frac {1}{80} x^{2}+\frac {1}{2640} x^{3}+\frac {1}{147840} x^{4}+\frac {1}{12566400} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{1} \left (1+x +\frac {1}{8} x^{2}+\frac {1}{168} x^{3}+\frac {1}{6720} x^{4}+\frac {1}{436800} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{x^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 86
AsymptoticDSolveValue[9*x^2*y''[x]+9*x*y'[x]-(1+3*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \sqrt [3]{x} \left (\frac {x^5}{12566400}+\frac {x^4}{147840}+\frac {x^3}{2640}+\frac {x^2}{80}+\frac {x}{5}+1\right )+\frac {c_2 \left (\frac {x^5}{436800}+\frac {x^4}{6720}+\frac {x^3}{168}+\frac {x^2}{8}+x+1\right )}{\sqrt [3]{x}} \]