Internal problem ID [6621]
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: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 47
dsolve(4*x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+(4*x^2-25)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-3 c_{2} \left (i x -\frac {1}{3} x^{2}+1\right ) {\mathrm e}^{-i x}+3 \,{\mathrm e}^{i x} \left (i x +\frac {1}{3} x^{2}-1\right ) c_{1}}{x^{\frac {5}{2}}} \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 59
DSolve[4*x^2*y''[x]+4*x*y'[x]+(4*x^2-25)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {\frac {2}{\pi }} \left (\left (-c_2 x^2+3 c_1 x+3 c_2\right ) \cos (x)+\left (c_1 \left (x^2-3\right )+3 c_2 x\right ) \sin (x)\right )}{x^{5/2}} \]