Internal problem ID [1318]
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: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \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: 41
Order:=6; dsolve(x^2*(3+4*x)*diff(y(x),x$2)+x*(11+4*x)*diff(y(x),x)-(3+4*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{2} x^{\frac {10}{3}} \left (1+\frac {32}{117} x -\frac {28}{1053} x^{2}+\frac {4480}{540189} x^{3}-\frac {15680}{4113747} x^{4}+\frac {401408}{185118615} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{1} \left (1+\frac {32}{7} x +\frac {48}{7} x^{2}+\mathrm {O}\left (x^{6}\right )\right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 67
AsymptoticDSolveValue[x^2*(3+4*x)*y''[x]+x*(11+4*x)*y'[x]-(3+4*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to \frac {c_2 \left (\frac {48 x^2}{7}+\frac {32 x}{7}+1\right )}{x^3}+c_1 \sqrt [3]{x} \left (\frac {401408 x^5}{185118615}-\frac {15680 x^4}{4113747}+\frac {4480 x^3}{540189}-\frac {28 x^2}{1053}+\frac {32 x}{117}+1\right ) \]