Question

Find the solution to the differential equation dy/dt​=0.5(y−150) if y=55 when t=0. y=

Answer 1

To solve the given first-order linear differential equation with the initial condition, we must separate the variables, integrate both sides, apply the initial condition, and then solve for the function y(t).

Step-by-step explanation:

The student has presented a first-order linear differential equation dy/dt = 0.5(y - 150), with an initial condition y(0) = 55. This is a separable differential equation, and we can solve it by integrating both sides.

1. Separate the variables by dividing both sides by (y - 150) and multiplying by dt.
2. Integrate both sides, introducing the constant of integration C on the side without the variable t.
3. Solve for C using the initial condition y(0) = 55.
4. Write the final solution function for y in terms of t.

Following these steps, we can find the function y(t) that satisfies the differential equation and the given initial condition.