Internal problem ID [4845]
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: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 35
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(36*x^2-1/4)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x \left (1-6 x^{2}+\frac {54}{5} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (1-18 x^{2}+54 x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 52
AsymptoticDSolveValue[x^2*y''[x]+x*y'[x]+(36*x^2-1/4)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (54 x^{7/2}-18 x^{3/2}+\frac {1}{\sqrt {x}}\right )+c_2 \left (\frac {54 x^{9/2}}{5}-6 x^{5/2}+\sqrt {x}\right ) \]