Internal problem ID [1426]
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: 10.
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 (3+10 x \right ) y^{\prime }+30 y x=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 48
Order:=6; dsolve(x^2*(1+x)*diff(y(x),x$2)-x*(3+10*x)*diff(y(x),x)+30*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = c_{1} x^{4} \left (1-\frac {2}{5} x +\mathrm {O}\left (x^{6}\right )\right )+\ln \relax (x ) \left (43200 x^{4}-17280 x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}+\left (-144-1440 x -7200 x^{2}-28800 x^{3}-90720 x^{4}+82944 x^{5}+\mathrm {O}\left (x^{6}\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 48
AsymptoticDSolveValue[x^2*(1+x)*y''[x]-x*(3+10*x)*y'[x]+30*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x^4-\frac {2 x^5}{5}\right )+c_1 \left (745 x^4-300 x^4 \log (x)+200 x^3+50 x^2+10 x+1\right ) \]