Solve the Initial Value Problem.

Question

dv/dt=9sqrt(t), y(1)=6

Answer 1

I think you probably meant to say v(1) = 6?

 

So,

 

dv = 9*sqrt(t)*dt = 9*t^1/2*dt

 

integrate both sides with respect to t and remembering the formula for integrating a power, 

 

v = 9*t^(3/2)/(3/2) + C

 

don't for get the C as we are dealing with an indefinite integral here. 

 

reducing gives v = 6*t^(3/2) + C

 

to solve for C, we use the initial conditions.  Put t = 1 and v = 6 gives, 6 = 6*1 + C.  This gives C = 0 and the solution of the problem is,

 

v = 6*t^(3/2)