Internal problem ID [5883]
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: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 23
dsolve(9*x^2*diff(y(x),x$2)+9*x*diff(y(x),x)+(x^6-36)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \BesselJ \left (\frac {2}{3}, \frac {x^{3}}{9}\right )+c_{2} \BesselY \left (\frac {2}{3}, \frac {x^{3}}{9}\right ) \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 42
DSolve[9*x^2*y''[x]+9*x*y'[x]+(x^6-36)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \text {Gamma}\left (\frac {1}{3}\right ) J_{-\frac {2}{3}}\left (\frac {x^3}{9}\right )+c_2 \text {Gamma}\left (\frac {5}{3}\right ) J_{\frac {2}{3}}\left (\frac {x^3}{9}\right ) \\ \end{align*}