What is a solution to the differential equation $\frac{dy}{dx}=4-6y$?

tophergopher3wo
2022-09-14
Answered

What is a solution to the differential equation $\frac{dy}{dx}=4-6y$?

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asked 2022-05-21

I am trying to solve the following differential equation using the Laplace Transform:

$L\frac{di}{dt}+Ri=E$

I have managed to reduce it to the following equation:

$I(s)=\frac{E}{sL(s+R/L)}$

But I'm having a problem with it from there. Can somebody help me solve this please? Any help would be much appreciated.

$L\frac{di}{dt}+Ri=E$

I have managed to reduce it to the following equation:

$I(s)=\frac{E}{sL(s+R/L)}$

But I'm having a problem with it from there. Can somebody help me solve this please? Any help would be much appreciated.

asked 2020-11-16

Solve differential equation
$(6x+1){y}^{2}dy/dx+3{x}^{2}+2{y}^{3}=0$ , y(0)=1

asked 2020-12-28

Solve differential equation

asked 2022-09-29

How do you solve for xy'−y=3xy given y(1)=0?

asked 2022-05-13

I've been trying to solve the following differential equation:

$3x+y(x)-2+\frac{dy(x)}{dx}(x-1)=0$

And I found out it's an exact differential equation, since it can be rearranged as $(3x+y(x)-2)dx+(x-1)dy=0$

Assuming that a function $U(x,y)=\frac{\mathrm{\partial}U}{\mathrm{\partial}x}dx+\frac{\mathrm{\partial}U}{\mathrm{\partial}y}dy=k$, (where $k\equiv $ constant) exists, I calculated it as:

$U(x,y)=\int (3x+y-2)dx+\int (x-1)dy=k$

And I got

$y(x)=\frac{-3{x}^{2}}{2(2x-1)}+\frac{2x}{2x-1}+\frac{k}{2x-1}$

But Mathematica says the solution is

$y(x)=\frac{-3{x}^{2}}{2(x-1)}+\frac{2x}{x-1}+\frac{k}{1-x}$

So either I assumed something which isn't correct or I made a mistake along the process. Where did I go wrong?

$3x+y(x)-2+\frac{dy(x)}{dx}(x-1)=0$

And I found out it's an exact differential equation, since it can be rearranged as $(3x+y(x)-2)dx+(x-1)dy=0$

Assuming that a function $U(x,y)=\frac{\mathrm{\partial}U}{\mathrm{\partial}x}dx+\frac{\mathrm{\partial}U}{\mathrm{\partial}y}dy=k$, (where $k\equiv $ constant) exists, I calculated it as:

$U(x,y)=\int (3x+y-2)dx+\int (x-1)dy=k$

And I got

$y(x)=\frac{-3{x}^{2}}{2(2x-1)}+\frac{2x}{2x-1}+\frac{k}{2x-1}$

But Mathematica says the solution is

$y(x)=\frac{-3{x}^{2}}{2(x-1)}+\frac{2x}{x-1}+\frac{k}{1-x}$

So either I assumed something which isn't correct or I made a mistake along the process. Where did I go wrong?

asked 2022-01-21

Solve the following first order differential equations.

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

asked 2022-01-19

The Runge Kutta method is known as:

a. An analytical method of solving first order differential equations.

b. An accurate method of solving first order differential equations.

c. A numberical method of solving first order differential equations.

d. A complex method of solving first order differential equations.

a. An analytical method of solving first order differential equations.

b. An accurate method of solving first order differential equations.

c. A numberical method of solving first order differential equations.

d. A complex method of solving first order differential equations.