Answer:
a.
Step-by-step explanation:
We are given that a solution
y= cos (kt) satisfied the differential equation
We have to find the value of k
a.y=coskt
Differentiate w.r.t x
Then we get
Again differentiate w.r.t x
(
Substitute the value in given differential equation
coskt cancel on both sides then we get
a.
b.We have to show that y=A sin kt + B cos kt is a solution to given differential equation for k=
Substitute the values of k
Then we get
Differentiate w.r.t x
Again differentiate w.r.t x
Then we get
Substitute the value of y'' and y in given differential equation
LHS=RHS
Hence, every function of the form
y=A cos kt +B sin kt is a s solution of given differential equation for k=
Where A and B are constants