Internal problem ID [4844]
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: 7.
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 (9 x^{2}-4\right ) y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 47
Order:=6; dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(9*x^2-4)*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \frac {c_{1} x^{4} \left (1-\frac {3}{4} x^{2}+\frac {27}{128} x^{4}+\mathrm {O}\left (x^{6}\right )\right )+c_{2} \left (\ln \relax (x ) \left (729 x^{4}+\mathrm {O}\left (x^{6}\right )\right )+\left (-144-324 x^{2}+\mathrm {O}\left (x^{6}\right )\right )\right )}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 54
AsymptoticDSolveValue[x^2*y''[x]+x*y'[x]+(9*x^2-4)*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (\frac {\left (9 x^2+8\right )^2}{64 x^2}-\frac {81}{16} x^2 \log (x)\right )+c_2 \left (\frac {27 x^6}{128}-\frac {3 x^4}{4}+x^2\right ) \]