All categories

3 years ago

True or False

Mathematics

1 answer:

DanielleElmas [232]3 years ago

6 0

Answer: False actually

You might be interested in

A Bernoulli differential equation is one of the form dxdy+P(x)y=Q(x)yn Observe that, if n=0 or 1, the Bernoulli equation is line

aleksandr82 [10.1K]

It's unclear whether the ODE is

$xy'+y=4xy^2$

$xy+y'=4xy^2$

If the first case, then divide through both sides by $y^2$ to get

$xy^{-2}y'+y^{-1}=4x$

then substitute $z=y^{-1}$ , so that $z'=-y^{-2}y'$ . Then

$-xz'+z=4x\implies-\dfrac1xz'+\dfrac1{x^2}z=\left(-\dfrac1xz\right)'=\dfrac4x$

$\implies-\dfrac1xz=\displaystyle\int\frac4x\,\mathrm dx$

$\implies z=-4x\ln|x|+Cx$

$\implies\boxed{y=\dfrac1{Cx-4x\ln|x|}}$

If the second, then dividing through by $y^2$ gives

$xy^{-1}+y^{-2}y'=4x$

The same substitution as before gives

$xz-z'=4x\implies e^{-x^2/2}z'-xe^{-x^2/2}z=\left(e^{-x^2/2}z\right)'=-4xe^{-x^2/2}$

$\implies e^{-x^2/2}z=\displaystyle-4\int xe^{-x^2/2}\,\mathrm dx$

$\implies z=4+Ce^{x^2/2}$

$\implies\boxed{y=\dfrac1{4+Ce^{x^2/2}}}$

5 0

3 years ago

List all the subsets of {1}

WITCHER [35]

Any set with one element, as is the case here, can have two subsets. Here, those subsets are the empty set {} and the whole set {1}.

4 0

3 years ago

4x^2 + 36 / 4x × 1 / 5x

stich3 [128]

Given with a polynomial 4X² + 36/4X *1/5X, we can combine terms with the same power. First, let us perform multiplication of the 2nd and 3rd terms such as the given become 4X² + 36/20X². Then, we can reduce 36 and 20 by 4 and the result is 4X² + 9/5X². We can now proceed combining the terms since they have same power and result will be same as below:
(20X^4 + 9)/5X²

3 0

3 years ago

Which of the following numbers are imaginary?

AlexFokin [52]

Answer:

Step-by-step explanation:

The numbers are not the things i is the square root i dunno how to explain iat but it is 1.25 square roots

7 0

3 years ago

Luigi is an urban planner. As an independent contractor, he charges $140 fee plus $25 per hour for each contract with the city.

Bess [88]

Answer:

D. Y = 25x + 140

Step-by-step explanation:

4 0

3 years ago