Question

Solve the initial value problem y ′ =2y with y(0)=7 y(t)= Here, and in future problems, your answer needs to be formatted like: 4exp(3t)−(7t+1)exp(−t)

Answer 1

To solve the initial value problem y′=2y with y(0)=7, we can use separation of variables.

Step-by-step explanation:

To solve the initial value problem y′=2y with y(0)=7, we can use separation of variables. Rearranging the equation, we have y′/y=2. Integrating both sides with respect to t, we get ln|y|=2t + C, where C is the constant of integration. Using the initial condition y(0)=7, we can solve for C by substituting t=0 and y=7 into the equation. We find that ln|7|=2(0) + C, which simplifies to C=ln|7|. Therefore, the solution to the initial value problem is y=7exp(2t), where exp is the exponential function.