Solve the initial value problem dydx=(x−2)(y−10),y(0)=5dydx=(x−2)(y −10),y(0)=5.
y=

The solution for the initial value problem is:

Step-by-step explanation:

We have the following initial value problem:

The first step is solving the differential equation. We can do this by the variable separation method. It means that every term with y in on one side of the equality, every term with x on the other side. So:

To find y in function of x, we integrate both sides.

Solving each integral separately

This one we solve by substitution

Now we have that:

To solve for y, we apply the exponential to both sides, since the exponential and ln are inverse operations:

means that when . So:

So, the solution for the initial value problem is:

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what is the image?

answer: x=3 and y=4

step-by-step explanation: