Internal problem ID [6628]
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: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 101
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+(2*x^2-64)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-16 \sqrt {2}\, c_{1} \left (x^{6}-75 x^{4}+1080 x^{2}-2520\right ) \operatorname {BesselJ}\left (1, \sqrt {2}\, x \right )-16 \sqrt {2}\, c_{2} \left (x^{6}-75 x^{4}+1080 x^{2}-2520\right ) \operatorname {BesselY}\left (1, \sqrt {2}\, x \right )+x \left (x^{6}-240 x^{4}+7200 x^{2}-40320\right ) \left (\operatorname {BesselJ}\left (0, \sqrt {2}\, x \right ) c_{1} +\operatorname {BesselY}\left (0, \sqrt {2}\, x \right ) c_{2} \right )}{x^{7}} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 30
DSolve[x^2*y''[x]+x*y'[x]+(2*x^2-64)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {BesselJ}\left (8,\sqrt {2} x\right )+c_2 \operatorname {BesselY}\left (8,\sqrt {2} x\right ) \]