What is a solution to the differential equation $\frac{dy}{dx}=2x$?

driliwra7
2022-09-15
Answered

What is a solution to the differential equation $\frac{dy}{dx}=2x$?

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asked 2022-01-21

Find the general solution of these first order differential equations

$\left(1\u2013x\right){y}^{\prime}={y}^{2}$

asked 2022-09-08

What is a solution to the differential equation $\frac{dy}{dx}=3y$?

asked 2022-06-25

If I have: $\dot{\sigma}(t)=-\gamma \sigma (t)$

where $\gamma $ is a constant, the solution is given by:

$\sigma (t)=\sigma (0){e}^{-\gamma t}$

Now what if I have the differential equation: $\dot{\sigma}(t)=-\gamma x(t)\sigma (t)$

Then is the solution given by:

$\sigma (t)=\sigma (0){e}^{-\gamma x(t)t}$

Or...?

where $\gamma $ is a constant, the solution is given by:

$\sigma (t)=\sigma (0){e}^{-\gamma t}$

Now what if I have the differential equation: $\dot{\sigma}(t)=-\gamma x(t)\sigma (t)$

Then is the solution given by:

$\sigma (t)=\sigma (0){e}^{-\gamma x(t)t}$

Or...?

asked 2022-02-17

Make use of vectors to re-write the following second order differential equation into a 1st order differential equation. (note: I do not need to solve it).

$2.1{x}^{-2}\frac{{d}^{2}y}{{dx}^{2}}-3{e}^{2x}{y}^{4}\frac{dy}{dx}=-6y$

where$y=4.2$ and $\frac{dy}{dx}=-3.1$ when $x=0.5$ .

Im not sure were to begin any help is greatly appreciated.

where

Im not sure were to begin any help is greatly appreciated.

asked 2022-06-11

I would like some help on comprehending this question as well as a push in the right direction. The question gave a system of first-order differential equation.

$x(t{)}^{\prime}=4x(t)-3y(t)+6{e}^{2t}$

$y(t{)}^{\prime}=4x(t)-6y(t)$

The question asked me to find the 2nd inhomogeneous equation that satisfies x(t). Does this mean the answer should all be in terms of x? I tried focusing on the x and differentiating it with respect to t.

so $x(t{)}^{\prime}=4x(t)-3y(t{)}^{\prime}+6{e}^{2t}$ becomes:

$x(t{)}^{\u2033}=4x(t{)}^{\prime}-3y(t{)}^{\prime}+12{e}^{2t}$

for simplicity sake, I will write x(t) as x and y(t) as y.

After that step, I replaced the y' in the x'' equation with the rearranged y' from the original question into the differentiated x' equation. This gives:

${x}^{\u2033}=4{x}^{\prime}-3(4x-6(\frac{1}{-3}({x}^{\prime}-4x-6{e}^{2t})+12{e}^{2t}$

this cancels down to:

${x}^{\u2033}=4{x}^{\prime}-12x+2{x}^{\prime}-8x$

but if you move everything to one side, it becomes

${x}^{\u2033}-6{x}^{\prime}+20x=0$

this is a second-order homogenous equation, so I don't quite know where I went wrong

$x(t{)}^{\prime}=4x(t)-3y(t)+6{e}^{2t}$

$y(t{)}^{\prime}=4x(t)-6y(t)$

The question asked me to find the 2nd inhomogeneous equation that satisfies x(t). Does this mean the answer should all be in terms of x? I tried focusing on the x and differentiating it with respect to t.

so $x(t{)}^{\prime}=4x(t)-3y(t{)}^{\prime}+6{e}^{2t}$ becomes:

$x(t{)}^{\u2033}=4x(t{)}^{\prime}-3y(t{)}^{\prime}+12{e}^{2t}$

for simplicity sake, I will write x(t) as x and y(t) as y.

After that step, I replaced the y' in the x'' equation with the rearranged y' from the original question into the differentiated x' equation. This gives:

${x}^{\u2033}=4{x}^{\prime}-3(4x-6(\frac{1}{-3}({x}^{\prime}-4x-6{e}^{2t})+12{e}^{2t}$

this cancels down to:

${x}^{\u2033}=4{x}^{\prime}-12x+2{x}^{\prime}-8x$

but if you move everything to one side, it becomes

${x}^{\u2033}-6{x}^{\prime}+20x=0$

this is a second-order homogenous equation, so I don't quite know where I went wrong

asked 2022-01-22

Explain why or why not determine whether the following statements are true and give an explanation or counterexample.

a. The differential equation y+2y

a. The differential equation y+2y

asked 2022-06-04

I am trying to evaluate the equation:

${y}^{\prime}=y({y}^{2}-\frac{1}{2})$

I multiplied the y over and tried to solve it in seperable form (M and N). The partial deritives did not work out to be equal to eachother so I am now stuck finding an integrating factor. Is this the right approach?

${y}^{\prime}=y({y}^{2}-\frac{1}{2})$

I multiplied the y over and tried to solve it in seperable form (M and N). The partial deritives did not work out to be equal to eachother so I am now stuck finding an integrating factor. Is this the right approach?