Internal problem ID [4860]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\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: 31
Order:=6; dsolve(16*x^2*diff(y(x),x$2)+32*x*diff(y(x),x)+(x^4-12)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{2} \left (1-\frac {1}{384} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (-2+\frac {1}{64} x^{4}+\mathrm {O}\left (x^{6}\right )\right )}{x^{\frac {3}{2}}} \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 40
AsymptoticDSolveValue[16*x^2*y''[x]+32*x*y'[x]+(x^4-12)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {1}{x^{3/2}}-\frac {x^{5/2}}{128}\right )+c_2 \left (\sqrt {x}-\frac {x^{9/2}}{384}\right ) \]