Question

Answer true or false without referring back to the text. The general solution of x2y'' + xy' + (x2 − 9)y = 0 is y = c1J3(x) + c2J−3(x).

True or False

Answer 1

solution Bessel's equation is Z dry d² +x dy (x²-02) y dat comparing the given differential equation y" + xy' +(22-9) -(2) 3 no with regun (1) , we get which is non-zero and non- integer. know that we the case no The when or n£ an integr complete solution equation may be expressed y = AJ, (x) + BJ, (x2) of the Bessel ag 3 where A and B are aytitary constants and ntak In () = kao (*)! +K+1) 2 -ntak In (x) = Mo Ek 2 and kao (k)! Sen+k+1) REMARKa when n is not a integer, Jon (x) is distinct from In (&). the general solution putting Hence is given by equnce) by n= 3

:. Y AJ3 (X) + BIZ (X) = or ly= G J3 (%) + G J3 (*) where G,Ğ are another arbitrary constant TRUE Hem
TRUE