Internal problem ID [4840]
Book: A FIRST COURSE IN DIFFERENTIAL EQUATIONS with Modeling Applications. Dennis G.
Zill. 9th edition. Brooks/Cole. CA, USA.
Section: Chapter 6. SERIES SOLUTIONS OF LINEAR EQUATIONS. Exercises. 6.3.1 page
250
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.024 (sec). Leaf size: 35
Order:=6; dsolve(4*x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+(4*x^2-25)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{5} \left (1-\frac {1}{14} x^{2}+\frac {1}{504} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (2880+480 x^{2}+120 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{\frac {5}{2}}} \]
✓ Solution by Mathematica
Time used: 0.01 (sec). Leaf size: 58
AsymptoticDSolveValue[4*x^2*y''[x]+4*x*y'[x]+(4*x^2-25)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {x^{3/2}}{24}+\frac {1}{x^{5/2}}+\frac {1}{6 \sqrt {x}}\right )+c_2 \left (\frac {x^{13/2}}{504}-\frac {x^{9/2}}{14}+x^{5/2}\right ) \]