Solve the differential equation dx/dt = -2(x-6)^(1/2) for t in terms of x given that x = 70 when t = 0.
First, manoeuvre variables so that we can integrate the equation.
1/(x-6)^(1/2) dx = -2 dt
Integrate the equation and add the constant.
2(x-6)^(1/2) = -2t +c
Solve for t.
t = -(x-6)^(1/2) - c
Substitute x = 70 when t = 0 to find the constant.
0 = -(70-6)^(1/2) - c
c = -8
Substitute c into our equation for t in terms of x.
t = 8 - (x-6)^(1/2)
LP
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