Internal problem ID [1319]
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: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {2 x^{2} \left (3 x +2\right ) y^{\prime \prime }+x \left (4+11 x \right ) y^{\prime }-\left (1-x \right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 47
Order:=6; dsolve(2*x^2*(2+3*x)*diff(y(x),x$2)+x*(4+11*x)*diff(y(x),x)-(1-x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x \left (1-\frac {5}{8} x +\frac {55}{96} x^{2}-\frac {935}{1536} x^{3}+\frac {4301}{6144} x^{4}-\frac {124729}{147456} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1-\frac {5}{4} x +\frac {25}{32} x^{2}-\frac {275}{384} x^{3}+\frac {4675}{6144} x^{4}-\frac {21505}{24576} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.046 (sec). Leaf size: 94
AsymptoticDSolveValue[2*x^2*(2+3*x)*y''[x]+x*(4+11*x)*y'[x]-(1-x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {935 x^{7/2}}{6144}+\frac {55 x^{5/2}}{384}-\frac {5 x^{3/2}}{32}+\frac {\sqrt {x}}{4}+\frac {1}{\sqrt {x}}\right )+c_2 \left (\frac {4301 x^{9/2}}{6144}-\frac {935 x^{7/2}}{1536}+\frac {55 x^{5/2}}{96}-\frac {5 x^{3/2}}{8}+\sqrt {x}\right ) \]