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- Solution of Exercise:2.2
- Solution of Exercise:2.3
- Solution of Exercise:2.4
- Solution of Exercise:2.5
- Solution of Exercise:3.1
- Solution of Exercise:4.1
- Solution of Exercise:4.2
- Solution of Exercise:4.3
- Solution of Exercise:4.4

In Problems 1–22, is the solution of the given differential equation by separation of variables. You may obtain a detailed answer by clicking on the question.

1: **Step by Step Solution**

Here we Solve by separation of variables dy/dx= sin5x. .

Given differential equation is:

(1)

We can separate the variables as follows:

(2)

Now, we can integrate both sides of the equation:

(3)

Integrating the left-hand side, we get:

(4)

where is the constant of integration.

For the right-hand side, we can use the substitution and to obtain:

(5)

where is another constant of integration. Substituting back , we have:

(6)

Substituting this back into our original equation, we have:

(7)

where and are constants of integration.

Therefore, the solution to the differential equation is:

(8)

where is the constant of integration.