Internal problem ID [6633]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(x^2*diff(y(x),x$2)+(x^2-2)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (\cos \left (x \right ) x -\sin \left (x \right )\right )}{x}+\frac {c_{2} \left (\cos \left (x \right )+\sin \left (x \right ) x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 21
DSolve[x^2*y''[x]+(x^2-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (c_1 j_1(x)-c_2 y_1(x)) \]