Internal problem ID [6958]
Book: Elementary differential equations. Rainville, Bedient, Bedient. Prentice Hall. NJ. 8th
edition. 1997.
Section: CHAPTER 18. Power series solutions. 18.6. Indicial Equation with Equal Roots.
Exercises page 373
Problem number: 11 (solved as direct Bessel).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }+y^{\prime }-y x=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x*diff(y(x),x$2)+diff(y(x),x)-x*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} \operatorname {BesselI}\left (0, x\right )+c_{2} \operatorname {BesselK}\left (0, x\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 26
DSolve[x*y''[x]+y'[x]-x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \operatorname {BesselJ}(0,i x)+c_2 \operatorname {BesselY}(0,-i x) \]