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:

312312

step-by-step explanation:

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1