Internal problem ID [1448]
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
III. Exercises 7.7. Page 389
Problem number: 32.
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 }-3 x \left (2 x^{2}+11\right ) y^{\prime }+\left (10 x^{2}+13\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 49
Order:=6; dsolve(9*x^2*diff(y(x),x$2)-3*x*(11+2*x^2)*diff(y(x),x)+(13+10*x^2)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = x^{\frac {1}{3}} \left (x^{4} \left (1+\frac {4}{27} x^{2}+\frac {7}{486} x^{4}+\mathrm {O}\left (x^{6}\right )\right ) c_{1}+c_{2} \left (\ln \relax (x ) \left (-\frac {32}{9} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\left (-144-32 x^{2}-\frac {8}{3} x^{4}+\mathrm {O}\left (x^{6}\right )\right )\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 62
AsymptoticDSolveValue[9*x^2*y''[x]-3*x*(11+2*x^2)*y'[x]+(13+10*x^2)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (\frac {7 x^{25/3}}{486}+\frac {4 x^{19/3}}{27}+x^{13/3}\right )+c_1 \left (\frac {2}{81} x^{13/3} \log (x)+\frac {1}{81} \left (x^2+9\right )^2 \sqrt [3]{x}\right ) \]