Question Solved1 Answer Solve the following ordinary differential equation in terms of Bessel functions. You may initially transform the given equation into the Bessel differential equation. Show the steps of transformation and find the transformed equation. Then, write the solution in terms of Bessel functions. y" + 4y = 0

BUFYKP The Asker · Advanced Mathematics

Transcribed Image Text: Solve the following ordinary differential equation in terms of Bessel functions. You may initially transform the given equation into the Bessel differential equation. Show the steps of transformation and find the transformed equation. Then, write the solution in terms of Bessel functions. y" + 4y = 0
More
Transcribed Image Text: Solve the following ordinary differential equation in terms of Bessel functions. You may initially transform the given equation into the Bessel differential equation. Show the steps of transformation and find the transformed equation. Then, write the solution in terms of Bessel functions. y" + 4y = 0
See Answer
Add Answer +20 Points
Community Answer
7CJW4Y The First Answerer
See all the answers with 1 Unlock
Get 4 Free Unlocks by registration

Answer: we have given the differential eqrationy^('')+4y=0" (1) "We have to transform (1) into Bessel diff. eqn, to do this we make an transform let y=ux^(1//2)- (2) where u is a function of x.by (2), (dy)/(dx)=x^(1//2)(dy)/(dx)+(1)/(2)x^(-1//2)yand (d^(2)y)/(delx^(2))=(1)/(2)x^(-1//2)(del y)/(dx)+x^(1//2)(d^(2)y)/(delx^(2))+(1)/(2)x^((1)/(2))(dy)/(del x)(-1)/(4)x^(-2)y=>(d^(2y))/(dx^(2))=x^(1//2)(d^(2)y)/(dx^(2))+x^(-1//2)(dy)/(dx)-(1)/(4)x^(-3//2u)Now put the value of (d^(2)y)/(dx^(2)) and y into the enn^(n) (1) we get{:[x^(1//2)(d^(2)y)/(delx^(2))+x^(-1//2)(del y)/(del x)-(1)/(4)x^(-3//2)y+4x^(1//2)u=0],[=>x^(2)(d^(2)y)/(delx^(2))+x(dy)/(del x)+(-(1)/(4))y^(')+4x^(2)y=0],[=>x^(2)(d^(2)u)/(dx^(2))+x(dy)/(del x)+(4x^(2)-(1)/(4))u=0]:}equ (3) is still not the Bessel diff. eq&qu ... See the full answer