Calculus initial value problem???

Question

determine that the given initial value problem has a unique question. 3(dx/dt) + 4t = 0, x(2) = -pi my answer is no

Answer 1

3(dx/dt) + 4t = 0

x(2) = -π

3(dx/dt) = -4t

dx/dt = -4t/3

x = -2t²/3 + C

x(2) = -π

-π = -2*2²/3 + C

-π = -8/3 + C

C = 8/3 - π

Unique solution is:

x = -2t²/3 + 8/3 - π

Note: This is not a yes / no question - they are saying "show that there is a unique solution"