Question

Solve the initial value problem dx/dt = x .

a) x(t) = eᵗ
b) x(t) = e²ᵗ
c) x(t) = e-ᵗ
d) x(t) = e-²ᵗ

Answer 1

The solution to the initial value problem dx/dt = x is x(t) = 0.

Step-by-step explanation:

The initial value problem dx/dt = x can be solved by separating variables and integrating both sides. When we do this, we find that the solution to the differential equation is x(t) = Ce^t, where C is a constant determined by the initial condition. Since x(0) = 0, we can substitute this into the equation to find that C = 0. Therefore, the solution to the initial value problem is x(t) = 0.