Internal problem ID [1431]
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: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} \left (1+2 x \right ) y^{\prime \prime }-2 x \left (4-x \right ) y^{\prime }-\left (5 x +7\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
Order:=6; dsolve(4*x^2*(1+2*x)*diff(y(x),x$2)-2*x*(4-x)*diff(y(x),x)-(7+5*x)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{4} \left (1-\frac {18}{5} x +\frac {39}{4} x^{2}-\frac {663}{28} x^{3}+\frac {13923}{256} x^{4}-\frac {7735}{64} x^{5}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (-144-\frac {405}{8} x^{4}+\frac {729}{4} x^{5}+\mathrm {O}\left (x^{6}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 67
AsymptoticDSolveValue[4*x^2*(1+2*x)*y''[x]-2*x*(4-x)*y'[x]-(7+5*x)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{\sqrt {x}}-\frac {35 x^{7/2}}{128}\right )+c_2 \left (\frac {13923 x^{15/2}}{256}-\frac {663 x^{13/2}}{28}+\frac {39 x^{11/2}}{4}-\frac {18 x^{9/2}}{5}+x^{7/2}\right ) \]