As we have seen, the total differential for a state function f (x, y) (an exact differential) can be written df =[∂f/∂x]y dx + [∂f/∂y]xdy
The Euler criterion for the exactness of a differential states that the differential
is exact if and only if
df = M(x, y)dx + N(x, y)dy = ∂N
[∂M/∂y]x = [∂N/∂x]y
State whether the following differentials are exact or inexact.
a) dq = CvdT + (RT/V) dV (assume that Cv and R are constants)
b) dS = (CV/T) dT + (R/V) dV (ditto)
As we have seen, the total differential for a state function f (x, y) (an exact...
What is the relationship between a state function and an exact differential? Match the items in the left column to the appropriate blanks in the sentences and the equations on the right. Reset Help In order for a function f(r,y) to be a state function, it must be possible to write the total differential df in the form df dr + dy If the form df as written exists, it is an exact differential
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, dF(, y) gives the differential equation. That is, level curves F(x,y) = C are solutions to the differential equation: dy 4x3 - y dx + 4y2 First rewrite as M(x,y) dic + N(x, y) dy = 0 where M(x,y) = and N(x,y) = If the equation is not exact, enter not exact, otherwise...
In this problem we consider an equation in differential form M dx + N dy = 0. (4x4 + 2y) dx +(- (2x + y2))dy = 0 Find My Nx = = If the problem is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) solutions to the differential equation. C, give implicit general If the equation is not exact, enter NE otherwise find...
(15 points) In this problem we consider an equation in differential form M dx + N dy = 0. (- (4xy2 + 4y)) dx +(- (4x²y + 4x))dy = 0 Find My N. If the problem is exact find a function F(x, y) whose differential, dF(x, y) is the left hand side of the differential equation. That is, level curves F(t, y) = C, give implicit general solutions to the differential equation. If the equation is not exact, enter NE...
Dif equations 4 4. a) Determine whether the following differential equation is exact. (x + 2y) dx + (2x - y)dy = 0 b) Find the general solution using the method of exact differentials.
Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose differential, dF (x, y) is the left hand side of the differential equation. That is, level curves F (x, y) = C are solutions to the differential equation: (4ху? — 4y)dx + (4х^у — 4х)dy %3D0 First: and N(x, y) : М/(х, у) 3 вху-4 = 8xy-4 If the equation is not exact, enter not exact, otherwise...
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. lf It is exact find a function F(xy whose differential, dF(x y is the left hand side of the differential equation. That is, level curves F x,y) = Care solutions to the differential equation First: M, (x, y) = | 3-e^x(cosy) and N(x, y)3-enx(cosy) If the equation is not exact, enter not exact, otherwise enter in F(x,y) here (-e1xsiny+3y)+(3x-excosy) (1 point) Use the "mixed...
3. DO NOT USE CALCULATOR for this problem! Find the EXACT VALUES for all the parts. Given the function f(x,y) (a) Calculate the total differential of z at the point (x, y, z) (b) Use the total differential to estimate the value of f(1+2(10200),-1 3(10-200). [ Hint : dz= 2(10-200) dy=_3(10-200)]. (c) Calculate the exact diffe ( f(1.-) I Note: total differentiala exact difference. ] rence of f(1+2(10-200)10 200))- (d) Find an equation for the plane s-L(x,y) tangent t(:-: f(z,y)...
Solve the exact differential equation (4 x y tsin x) dx + (x" - Y) dy = 0
(1 point) Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x, y) whose differential, d F(x, y) is the left hand side of the differential equation. That is, level curves F(x, y) = C are solutions to the differential equation (-3e* sin(y) + 4y)dx + (4x – 3e* cos(y))dy = 0 First, if this equation has the form M(x, y)dx + N(x, y)dy = 0: My(x, y)...