Linear Differential Equations

Question

Find the particular antiderivative that satisfies the following conditions:

dx/dt=4e(^t)−2; x(0)=7.



I know dx/dt of 4e^(t)-2 is 4e^(t)-2t, but I do not know what to do with the x(0)=7.

Answer 1

x(t)=4e^t-2t+C (C is constant of integration)

x(0)=7=4+C

C=3

Complete solution: x(t)=4e^t+2t+3