Use an integrating factor to solve the following first order linear ode. xy' + 2y = 3x, y(1) = 3 find the end behavior of y as x rightarrow infinity.

Solution -->

when x --> infinity the y goes to infinity too.

Step-by-step explanation:

We have the eq.

with y(1) = 3. So a reconfiguration o this last one equation can be like:

so is of the form y'+p(x) y = f(x), where the integral factor is given by:

is,

Multiplying the whole equation with this integral factor we can write the expression:

and from this we obtain,

So when y(x=1) = 3, c = 2 and the complete solution can be writen as:

.

And we can see that when x --> infinity the second term of the solution is practically zero and the first is infinity so y also goes to infinity when x does.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.