What is a solution to the differential equation $\frac{dy}{dx}=\frac{1}{x}+1$?

gemauert79
2022-09-26
Answered

What is a solution to the differential equation $\frac{dy}{dx}=\frac{1}{x}+1$?

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Karli Moreno

Answered 2022-09-27
Author has **7** answers

this is already separated out

$y\prime =\frac{1}{x}+1$

$\int y\prime dx=\int \frac{1}{x}+1dx$

$\Rightarrow \int dy=\int \frac{1}{x}+1dx$

$y=\mathrm{ln}x+x+C$

$y\prime =\frac{1}{x}+1$

$\int y\prime dx=\int \frac{1}{x}+1dx$

$\Rightarrow \int dy=\int \frac{1}{x}+1dx$

$y=\mathrm{ln}x+x+C$

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What is the general solution of the differential equation $\frac{dy}{dx}-2y+a=0$?

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What is a solution to the differential equation $\frac{dx}{dt}=t(x-2)$?

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What is a general solution to the differential equation $y\prime +2xy=2{x}^{3}$?

asked 2022-06-11

I'm trying to solve an initial value problem. I know how to do the problem once integrated but solving the differential equation is where I'm finding trouble.

$dy/dx=3+\sqrt{2y+17x-3}$

I'd thought that maybe squaring both sides will get rid of the square root but that doesn't work so I was hoping someone would point me in the right direction of how to go about seperating $y$ and $x.$

$dy/dx=3+\sqrt{2y+17x-3}$

I'd thought that maybe squaring both sides will get rid of the square root but that doesn't work so I was hoping someone would point me in the right direction of how to go about seperating $y$ and $x.$

asked 2022-04-10

For every differentiable function $f:\mathbb{R}\to \mathbb{R}$, there is a function $g:\mathbb{R}\times \mathbb{R}\to \mathbb{R}$ such that $g(f(x),{f}^{\prime}(x))=0$ for every $x$ and for every differentiable function $h:\mathbb{R}\to \mathbb{R}$ holds that

being true that for every $x\in \mathbb{R}$, $g(h(x),{h}^{\prime}(x))=0$ and $h(0)=f(0)$ implies that $h(x)=f(x)$ for every $x\in \mathbb{R}$.

i.e every differentiable function $f$ is a solution to some first order differential equation that has translation symmetry.

being true that for every $x\in \mathbb{R}$, $g(h(x),{h}^{\prime}(x))=0$ and $h(0)=f(0)$ implies that $h(x)=f(x)$ for every $x\in \mathbb{R}$.

i.e every differentiable function $f$ is a solution to some first order differential equation that has translation symmetry.

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 2022-09-11

How do you find all solutions of the differential equation $\frac{{d}^{2}y}{{dx}^{2}}=0$?