Question

Find the general solution of the differential equation. Primes denote derivatives with respect to x. y(4)+8y′′+16y=0 4. Solve the initial value problem. Primes denote derivatives with respect to x. 3y(3)+2y′′=0;y(0)=−1,y′(0)=0y′′(0)=1

Answer 1

To find the general solution of the differential equation, assume the general form of the solution.

Step-by-step explanation:

To find the general solution of the given differential equation: y(4) + 8y'' + 16y = 0,

we can assume the general form of the solution in regions I and III to be:

y(x) = C1eλ1x + C2eλ2x + C3cos(αx) + C4sin(αx)

where λ1, λ2, α, C1, C2, C3, C4 are arbitrary constants to be determined.