MATHEMATICS II

Therefore, the correct answer is B.

This is a separable differential equation hence we may write

This may be rewritten as

if we say

then the solution is

The correct answer is A.

Then the solution can be written as

If we use the initial condition we get that

Thus, we can write the solution as:

Thus, the correct answer is D.

and substitute it into the differential equation. Then the characteristic equation is

So, the general equation can be written as

The correct answer is E.

If we say

We know that

Cancelling the factor

and taking the logarithms of both sides

is found as

Hence, we have,

Lastly, to find

we will use

Thus, 

The correct answer is A.

into suggested equations, we find that the only equation that is satisfied is (B).

The correct answer is B.

Then

Integrating by parts

so

From initial condition

Thus, the solution

The correct answer is C.

The correct answer is E.

and substitute it into the differential equation. Then the characteristic equation is

We can write the solution like

Using initial conditions

we have

Hence

The correct answer is D.

Therefore, the general solution is . From initial condition y(0)=1, hence 1=C∙1 ⇒ C=1
Thus, the solution .

The characteristic equation ⇒ . The general solution .

Integrating factor  Integrating by parts 

Therefore, the general solution is . From initial condition y(0)=-2, hence -2=C+1/2⇒ C=-5/2
Thus, the solution .

 Integrating factor 

 The general solution