# How do you solve the differential equation #dy/dt = 2y - 10#?

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This is a first-order linear ordinary differential equation. To solve it, you can use the method of separation of variables. Rearrange the equation to isolate y terms on one side and t terms on the other side. Then integrate both sides with respect to their respective variables and solve for y. Here's how you do it:

dy/dt = 2y - 10 dy = (2y - 10) dt

Now, separate the variables:

dy / (2y - 10) = dt

Integrate both sides:

∫(1 / (2y - 10)) dy = ∫dt

On the left side, integrate with respect to y, and on the right side, integrate with respect to t:

(1/2) * ln|2y - 10| = t + C

Where C is the constant of integration.

Now, solve for y:

ln|2y - 10| = 2t + C

Raise both sides as powers of e:

|2y - 10| = e^(2t + C)

Remove the absolute value:

2y - 10 = ± e^(2t + C)

Now, solve for y:

y = (1/2) * (e^(2t + C) + 10)

This is the general solution to the given differential equation.

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