cistG
2020-12-30
Answered

Solve differential equation$x{y}^{\prime}+3y=6{x}^{3}$

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Usamah Prosser

Answered 2020-12-31
Author has **86** answers

Divide by 'x'

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Jeffrey Jordon

Answered 2021-12-25
Author has **2262** answers

Answer is given below (on video)

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Find y" by implicit differentiation.

${x}^{2}+4{y}^{2}=4$

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Find the first partial derivatives of the function.

$z=x\mathrm{sin}\left(xy\right)$

asked 2022-05-21

My Problem is this given System of differential Equations:

$\dot{x}=8x+18y$

$\dot{y}=-3x-7y$

I am looking for a gerenal solution.

My Approach was: i can see this is a System of linear and ordinary differential equations. Both are of first-order, because the highest derivative is the first. But now i am stuck, i have no idea how to solve it. A Transformation into a Matrix should lead to this expression:

$\overrightarrow{y}=\left(\begin{array}{cc}8& 18\\ -3& -7\end{array}\right)\cdot x$

or is this correct:

$\overrightarrow{x}=\left(\begin{array}{cc}8& 18\\ -3& -7\end{array}\right)\cdot y\text{?}$

But i don't know how to determine the solution, from this point on.

$\dot{x}=8x+18y$

$\dot{y}=-3x-7y$

I am looking for a gerenal solution.

My Approach was: i can see this is a System of linear and ordinary differential equations. Both are of first-order, because the highest derivative is the first. But now i am stuck, i have no idea how to solve it. A Transformation into a Matrix should lead to this expression:

$\overrightarrow{y}=\left(\begin{array}{cc}8& 18\\ -3& -7\end{array}\right)\cdot x$

or is this correct:

$\overrightarrow{x}=\left(\begin{array}{cc}8& 18\\ -3& -7\end{array}\right)\cdot y\text{?}$

But i don't know how to determine the solution, from this point on.

asked 2022-01-18

I want to get a particular solution to the differential equation

$y{}^{\u2033}+2{y}^{\prime}+2y=2{e}^{x}\mathrm{cos}\left(x\right)$

and therefore I would like to 'complexify' the right hand side. This means that I want to write the right hand side as$q\left(x\right){e}^{\alpha x}$ with q(x) a polynomial. How is this possible?

and therefore I would like to 'complexify' the right hand side. This means that I want to write the right hand side as

asked 2021-09-17

find the Laplace transform of f (t).

$f\left(t\right)=t\mathrm{sin}3t$

asked 2022-01-22

Solving an ordinary differential equation:

Prove if${y}^{\prime}\left(t\right)+3y\left(t\right)=6t+5,y\left(0\right)=3$ , then $y\left(t\right)=2{e}^{-3t}+2t+1$ .

Prove if

asked 2022-04-12

What method would you use to solve:

$(1+{x}^{2})\frac{\mathrm{d}y}{\mathrm{d}x}=1+{y}^{2}\phantom{\rule{thickmathspace}{0ex}};\phantom{\rule{2em}{0ex}}y(2)=3$

I am asking this because I only know two methods of solving the DEs - separation of variables and integrating factor. Since the separation of variables does not work here, I tried integrating factor, however, I don't know what to do with the y2, because for the IF to work I need to get y on its own $\frac{\mathrm{d}y}{\mathrm{d}x}+P(x)y=Q(x)$)

What method do I use to solve this?

$(1+{x}^{2})\frac{\mathrm{d}y}{\mathrm{d}x}=1+{y}^{2}\phantom{\rule{thickmathspace}{0ex}};\phantom{\rule{2em}{0ex}}y(2)=3$

I am asking this because I only know two methods of solving the DEs - separation of variables and integrating factor. Since the separation of variables does not work here, I tried integrating factor, however, I don't know what to do with the y2, because for the IF to work I need to get y on its own $\frac{\mathrm{d}y}{\mathrm{d}x}+P(x)y=Q(x)$)

What method do I use to solve this?