I'm trying to write a code to implement he backwards Euler method to integrate the equation of motion. The sticking point seems to be that the acceleration is due to drag, and thus is dependent on the new position and velocity.
I understand the method to be:
v_{i+1}=v_{i}+a_{i+1}δ...
I have the next function: z^3-2xz+y=0 and I want to find taylor expansion of z(x,y) at the point (1,1,1), obviously I need to define F(x,y,z) as above and use the implicit function theorem to calculate the derivatives of z(x,y), but I want mathematica to compute this to me.
I tried the Series...
Homework Statement
Find dy/dx in terms of x and y if..
x2-√(xy)+y2=6
Homework Equations
The Attempt at a Solution
so I started by..
x2-√(xy)+y2=6
deriving the LHS
2x+2y(dy/dx)-1/2(xy)-1/2(1(y)+x(dy/dx))
Simplifying the last term...
Homework Statement
use implicit differentiation to find an equation of the tangent line to the curve a the given point.
y^2(y^2-4) = x^2(x^2-5)
at (0,-2)
Homework Equations
y^2(y^2-4) = x^2(x^2-5)
The Attempt at a Solution
I got dy/dx to be (3x^2-10x)/(4y^3-8y)
but...
Hello. I know how to do implicit differentiation taught in calculus 1, but I'm confused by something regarding it.
Take the example:
y3+y2-5y-x2=4
If we do implicit differentation we get:
3y2(dy/dx)+2y(dy/dx)-5(dy/dx)-2x=0
dy/dx=2x/(3y2+2y-5)
Now, it makes sense how to...
Implicit isomorphism involved in extension/sub fields/structures?
This has been bugging me for a while. I'm pretty sure I'm correct but I'd just like to verify to put my mind at ease. I'd like to know if there is an implicit isomorphism involved when we say, for example, F is a substructure of...
Homework Statement
Its not homework, i have the answer I am just having a hard time wrapping my head around the concept of differentiating implicitly defined functions.
the question was: x^3+y^3=3xy, find the equation of the tangent line at the point (3/2,3/2).
Homework Equations...
Homework Statement
[SIZE="4"]
2x^{3}-3x^{2}y+2xy^{2}-y^{3}=2
Homework Equations
The Attempt at a Solution
[SIZE="4"]
6x^{2}-(6xy+3x^{2}y')+(2y^{2}+4xyy')-3y^{2}y'=0
y'=\frac{-6x^{2}+6xy-2y^{2}}{-3x^{2}y+4xy-3y^{2}}
My text's solution is the same answer but with every every...
Homework Statement The electrical potential can be described by the following equation:
V= 200/(x2 + y2 )1/2 find dV when x=2 and y=1
Homework Equations
n/a
The Attempt at a Solution
dv/d(x,y) = ∂/∂x + ∂/∂y
=200/(x2 + y2)(1/2) +200/(x2 + y2)(1/2)
replace variables with C where...
Homework Statement
I am suppose to find the second derivative implicitly of the function y^2 = x^3. I find the first derivative to be dy/dx = 3x^2/2y, but shortly find myself having difficulty in the second derivation. My steps for the second derivative is in the file attached; there are a few...
Homework Statement
Find the equations of the lines that pass through (0,0) and are tangent to x^2 - 4x + y^2 + 1 = 0
My confusion
I've been given a problem of this sort recently, except now it involves implicit differentiation. I know "how" to get to the correct answer. I just...
I tried deriving this one on my own and I'm just not understanding where the dx/dx term comes from. I'm looking dy/dx.
Starting with F(x,y) = 0:
\frac{\partial{F}}{\partial{x}}\frac{dx}{dx} + \frac{\partial{F}}{\partial{y}}\frac{dy}{dx} = 0
It seems redundant to say dx/dx when it turns out to...
Use implicit differentiation to find the slope of the tangent line to the curve at the specified point.
3(x^2 + y^2)^2 = 25(x^2 - y^2) ; (2,1)
This is where I'm stuck:
I know how to get up to the first equation...and I know how to get to the final answer from the second equation, but I...
Implicit differentiaion using the number "e" (lon-capa)
Hello~ :3 this is my first time posting here, so I hope I didn't do anything wrong. I'm currently in Calculus 1, university level, and I have to enter all my answers using lon-capa (evil evil program). In lon-capa:
*= multiplication...
Hello,
I need help writing a MATLAB program to solve a heat transfer problem implicitly. For some reason this is very confusing to me. The problem is stated below. Any help is greatly appriciated. Let me know if you need a little more info.
I need to write a program to solve this...
Homework Statement
The problem statement is to use Fortran 95 to code a forward time, centered space numerical solution to the 1-D (x-direction) Advection-Dispersion Equation:
dc/dt = u(dc/dx) + D(d2c/dx2) - kc
where c is the concentration of contaminant, u is the advecting velocity, D is...
Homework Statement
Find the coordinates of the stationary points on the curve:
x^3 + (3x^2)(y) -2y^3=16
Homework Equations
Stationary points occur when the first derivative of y with respect to x is equal to zero
The Attempt at a Solution
I implicitly differentiated the...
Can anyone check if this argument works. I just made up this problem to check if I understand what's going on.
Consider F = xy*e^x + y*e^y = K. I want to see if there is a unique solution.
Fy = x*e^x + y*e^y + e^y.
Since we are on the surface x*e^x + y*e^y = K.
So if K >= 0 then...
Homework Statement
Find an equation of the tangent line to the curve xe^y+ye^x=1 at point (0,1).
Homework Equations
I do not recall seeing the Implicit Function Theroem before, I even went back in my book (Stewart Calculus 6th) to check. I found this post but it does not help me...
I was working two different but superficially related problems, and noticed that if I did something that is generally not allowed, the results were connected by a negative sign. My questions are whether this will always turn out this way, and if so, why.
The two problems were
(A)...
Hello! I was wondering how I could find the following derivatives from the given function using Jacobian determinants.
f(u,v) = 0
u = lx + my + nz
v = x^{2} + y^{2} + z^{2}
\frac{∂z}{∂x} = ? (I believe y is constant, but the problem does not specify)
\frac{∂z}{∂y} = ? (I...
Homework Statement
Given that the surface (x**5)(y**2)+(y**5)(z**3)+(z**3)(x**2)+4xyz=7 has the equation z=f(x,y) in a neighbourhood of the point (1,1,1) with f(x,y) differentiable, find the derivatives
(∂**2f)/(∂x**2) at (1,1)
Homework Equations
The Attempt at a Solution
I...
Hi all,
i am beginner in fortran and linux. I have wrote codes for 1d scalar wave as below:
SUBROUTINE fd1d (x_num,x1,x2,t_num,t1,t2,c,u_x1,u_x2,u_t1,ut_t1,u)
implicit none
integer (kind=2) t_num,x_num,t,x
real (kind=4)...
Homework Statement
Derivate y with regards to x, \frac{dy}{dx}
2xy+y^2-4x=10
Homework Equations
The Attempt at a Solution
I am not very good at differentiation, so I haven't got off to a good start, really.
I guess I can differentiate y^2 and -4x "the usual way", but I am kind of stuck with...
Hi!
I'm trying to implement an implicit scheme for the continuity equation.
The scheme is the following:
http://img28.imageshack.us/img28/3196/screenshot20111130at003.png
With \rho being the density, \alpha is a weighing constant. d is a parameter that relates the grid spacing to the...
If, with y a function of x, I have the equation x2-5xy+3y2 = 7, then by implicit differentiation, I get that dy/dx = (2x-5y)/(5x-6y). This equals zero everywhere on the straight line y=(2/5)x except at the origin. This would seem to indicate stationary points everywhere on that line, which is...
Homework Statement
z^{3}x+z-2y-1=0
xz+y-x^{2}+5=0
Define z as a function of x, find z'.
Homework Equations
I guess the two equations above...
The Attempt at a Solution
Well, I just differentiated the first one with respect to x and got:
3z^{2}xz'+z^{3}3+1=0
z' = \frac{-1-z^{3}{3z^{2}x}...
Homework Statement
Find y' in
e^(x/y)=x-y
2. The attempt at a solution
I tried to differentiate it by changing it so that there would be a natural log (as seen in my attachment). However the end result is not the same as the answer key.
How the answer key did it was they used the...
Homework Statement
Q 50: The ellipse 3x2 +2y2 = 5 and y3 = x2
HINT: The curves intersect at (1,1) and (-1,1)
Two families of curves are said to be orthogonal trajectories (of each other) if each member of one family is orthogonal to each member of the other family. Show that the families of...
How do you go about solving implicit equations for y in terms of x that look like these?
y2 + yx = 1
and
y3 + yx = 1
or even more complicated implicit equations.
I'm taking AP Calculus AB this year and am just curious how this is done.
Here are the solutions from Wolframalpha...
Hello,
Can someone tell me if what I am doing is correct. I am trying to solve this equation of 0 = n ( p - p0 ) where n, p, and p0 are points on the plane. Assume this is a 2D dimension (x,y). Is this the correct way of calculating this equation.
0 = nx (px - p0x) + ny (py + p0y)...
Homework Statement
Determine the equation of a tangent line to a curve at the given point.
3x2+xy+2y2=36 , P(2,3)
Homework Equations
The Attempt at a Solution
3x2+xy+2y2 = 36
finding the derivatives of each term I get:
6x+xy'+y+4yy' = 0
xy'+4yy' = -6x-y
y'(x+4y) =...
How would one go about solving for one variable for an implicit Euler's method such as this:
I am completely lost...all I know is the value of U and dT
Un+1 = Un + (dU/dT)|n+1dT
Vn+1 = Vn + (dV/dT)|n+1dT
The equation is:
x2 dy/dx= y - xy
IC (initial conditions): y(-1) = -1 (This is used to solve for C)
Must first separate the variables x and y and then integrate them and solve for y, but I got stuck...
x2dy = (y - xy)dx
x2dy = y(1-x)dx
dy= y(1-x)dx/x2 <-- not sure what to do with the y now...
the problem is to find y'' or d2y / d2x
the equation is y2 = x2
first i found the first derivative dy/dx = 2x / 2y = x / y
then i found the second using the quotient rule and got
y'' = (y - x(dy/dx)) / y2
i plugged in y' into y'' and got
y'' = (y - (x2/y)) / y2
but then I am...
I'm given:
1. \frac{dX}{dt}=(X-1)(1-2X)
2. ln(\frac{2X-1}{X-1})=t
and asked to verify that it is an implicit solution to the first order DE given.
I successfully derived the second equation there to get:
\frac{dX}{dt}=\frac{-1}{(2X-1)(X-1)}
So now what? I tried several things and...
Homework Statement
(b) Find the differential equation for which –4xy3 + 4xy3sin(x) = –1 is an implicit solution on the interval (0, pi/2). Write your answer in the form dy/dx = f (x,y) where f (x, y) depends on both x and y.
The Attempt at a Solution
I'm not too sure on how to go about...
Hello,
recently, I have found so called Batman graph and equation, which basically plots Batman sign.
I have even found Python code that plots this implicit equation.
Code can be found here:
.
And the equation is given here:
[url]http://i.imgur.com/CNy9J.jpg
If you look closelx...
Homework Statement
find the d^2y/dx^2 if y^3 + y = 2 cos x at the point (0,1)
Homework Equations
The Attempt at a Solution
my dy/dx = (-2 sin x)/(3y^2 + 1)
I don't know how to find d^2y/dx^2?
And when and how will I use the oint (0,1)?
Homework Statement
Consider the curve satisfying the equation 2(x+1)^(tanx)=(y^2)cosx+y and find dy/dxHomework Equations
(tanx)'=sec^2x
(lnx)'=1/xThe Attempt at a Solution
I've tried taking the natural log of both sides and then taking d/dx of both sides but something seems to go wrong with...
Hi,
I am trying to write a code for an equation which looks like this:
\frac{\partial{y}}{\partial{t}}=f(x,y,t) -y(x^{n+1}-x^{n})
where n is the time step number. I have no idea how I can go on about solving (approximating the solution) to this problem. Any hints would be appreciated...
Homework Statement
A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30 degrees. At what rate is the distance from the plane to the radar station increasing a minute later?
Homework Equations
a2+b2=c2The...
I don't think I fully understand implicit differentiation. I have read my textbook and watched many videos, and I think I will get an A on my test on this solely by memorizing the rules, but I would really like to understand this topic. From what I know, you are supposed to use implicit...
Homework Statement
x^{3}y + y^{3}x = 30
Homework Equations
-
The Attempt at a Solution
My understanding is that I'm supposed to take the derivative of each side and try to solve for y'.
But, I don't know how to treat the y when I am differentiating it, to a power or whatever...