# Math

posted by .

For the harmonic potential V(x,y) = x^2 + y^2

a) Find the total differential, dV.
For this I got dV = 2x.dx + 2y.dy

b) Given that -dV = F(x).dx + F(y).dy, where F(x) and F(y) is the force in the x and y direction, respectively, write a differential equation describing the change of potential energy, V(x), with position x.

I am really not sure about this. Should I integrate the whole equation and then differentiate with respect to x?

## Similar Questions

1. ### Differential Equations

Find the general solution of the differential equation specified. 1) dy/dt= 1/(ty+1+y+1) 2) dy/dx=sec y I got y(x)=arcsin(x) for the second one. I'm not sure what to do with the first one.
2. ### Harmonic Oscillation

The velocity of a certain simple harmonic oscillator is given by: v=-(12m/s)sin [(6.0rad/s)t]. What is the amplitudeof the simple harmonic oscillator. Please show your work.
3. ### Physics

For the harmonic potential V(x,y) = x^2 + y^2 a)Find the total differential, dV. b) Show that dV is exact c) Given that -dV = Fx.dx + Fy.dy where Fx and Fy is the force in the x and y direction, respectively, write a differential equation …
4. ### Physics

A copper wire with a criss section of 5 mm^2 and 2 km long has an effective resistance of 2Ohms. a) Find the power lost in this wire if 10000 W of power is put through it with 120 V of potential. [hint: use P=VI to get current first …
5. ### math

find the differential of dy of the given function. y=3x-4sec(2x-1) The answer i got was dy=(3-8sec(2x-1)tan(2x-1))dx I am not entirely certain i got this correct. if you could check this for me, it would be a big help. :)
6. ### Math

a weight of mass m is attached to a spring and oscillates with simple harmonic motion. By Hooke's Law, the vertical displacement, y(t) satisfies the differential equation dy/dt=sqrt(k/m)*sqrt(A^2-y^2) where A(Fixed) is the maximum …
7. ### Math

Hey guys I need some help with this question PLZ: A telecommunications company offers a rental deal which costs \$30 per month plus 50c per call. a) Find the total cost (T1) for making x calls in a given month b)Find the total cost …
8. ### Trig Help

Given the equation for simple harmonic method d=1.3cos(3pi/4 t) answer the following questions: a)Find the maximum displacement. 1.i got 1.3 b)Find the frequency and length of the pendulum c)Calculate the value of d when t=3 i got …
9. ### Calculus!!

Consider the differential equation given by dy/dx = xy/2. A. Let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on the slope field, how does the value of f(0.2) compare to f(0)?
10. ### Calculus

Consider the differential equation dy/dx = x^2(y - 1). Find the particular solution to this differential equation with initial condition f(0) = 3. I got y = e^(x^3/3) + 2.

More Similar Questions