Internal problem ID [5874]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 6 SERIES SOLUTIONS OF LINEAR EQUATIONS. 6.4 SPECIAL
FUNCTIONS. EXERCISES 6.4. Page 267
Problem number: 9.
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 (25 x^{2}-\frac {4}{9}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(25*x^2-4/9)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \BesselJ \left (\frac {2}{3}, 5 x \right )+c_{2} \BesselY \left (\frac {2}{3}, 5 x \right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 26
DSolve[x^2*y''[x]+x*y'[x]+(25*x^2-4/9)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 J_{\frac {2}{3}}(5 x)+c_2 Y_{\frac {2}{3}}(5 x) \\ \end{align*}