Find the directional derivative of f at the given point in the direction indicated by the angle $\theta .f(x,y)={e}^{x}\mathrm{cos}y,(0,0),\theta =\frac{\pi}{4}$

Ernstfalld
2021-09-08
Answered

Find the directional derivative of f at the given point in the direction indicated by the angle $\theta .f(x,y)={e}^{x}\mathrm{cos}y,(0,0),\theta =\frac{\pi}{4}$

You can still ask an expert for help

Daphne Broadhurst

Answered 2021-09-09
Author has **109** answers

At the given condition:

asked 2022-01-20

Who know?

Solve the following first order differential equations. Use any method:

$2{x}^{2}dx-3x{y}^{2}dy=0;\text{}y\left(1\right)=0$

Solve the following first order differential equations. Use any method:

asked 2021-02-24

Solve differential equation

asked 2022-02-16

Suppose we have

$\frac{dy}{dx}+f\left(x\right)y=r\left(x\right)$

and it has two solutions${y}_{1}\left(x\right)$ and ${y}_{2}\left(x\right)$ then how to prove that solution of differential equation

$\frac{dy}{dx}+f\left(x\right)y=2r\left(x\right)$

Will be${y}_{1}\left(x\right)+{y}_{2}\left(x\right)$ ? I think given differential equations is linear first order equation so its solution will be

$y.{e}^{\int f\left(x\right)dx}=\int r.{e}^{\int f\left(x\right)dx}dx$

now do I establish two solution as$y}_{1$ and $y}_{2$ out of this equation?

and it has two solutions

Will be

now do I establish two solution as

asked 2022-04-12

Is there any possibility to convert first order differential equation to second order differential equation?

I have a system of first order differential equations as below and i need the right hand side of the second order form of this first order equation. (if possible)

$\frac{du(t)}{dt}=[t{u}_{2}(t);4{u}_{1}(t{)}^{3/2}]$

Any help would be appreciated.

I have a system of first order differential equations as below and i need the right hand side of the second order form of this first order equation. (if possible)

$\frac{du(t)}{dt}=[t{u}_{2}(t);4{u}_{1}(t{)}^{3/2}]$

Any help would be appreciated.

asked 2022-01-20

Solve and find the soltion to the first order differential equation:

$x\frac{dy}{dx}+y={e}^{x},\text{}\text{}x0$

asked 2022-03-29

Sketch grapf of f(y)=y for dy\dt = ay+by^2,a>0,b>0,y>0

asked 2020-12-28

Solve differential equation