Question

What is the general solution to the following ODE that is valid over the domain 0≤x≤1 u²d²g/du²​+udg/du​+(u²−16)g=0 a. g=J₁₆​(u) b. g=K₁​J₄​(u)+K₂​J₋₄​(u) c. g=K₁J₄(u)+K₂Y₄​(u) d. g=KJ₄​(u)

Answer 1

The general solution to the given ODE is g = K₁J₄(u) + K₂J₋₄(u).

Step-by-step explanation:

The general solution to the given ordinary differential equation (ODE) is:

g = K1J4(u) + K2J-4(u)

where J4(u) and J-4(u) are Bessel functions of the first kind with order 4 and -4 respectively, and K1 and K2 are constants.