Internal problem ID [4861]
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: 26.
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 (16 x^{4}+3\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 31
Order:=6; dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(16*x^4+3)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \sqrt {x}\, \left (\left (1-\frac {1}{5} x^{4}+\mathrm {O}\left (x^{6}\right )\right ) x c_{1}+\left (1-\frac {1}{3} x^{4}+\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 40
AsymptoticDSolveValue[4*x^2*y''[x]-4*x*y'[x]+(16*x^4+3)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\sqrt {x}-\frac {x^{9/2}}{3}\right )+c_2 \left (x^{3/2}-\frac {x^{11/2}}{5}\right ) \]