Step 6 Since F is conservative, we know that f,(x, y, z) = 12yz2 Therefore, h'(z) = 0

Q: an integrating factor for the DE dy+ydx=e3x dx is  1)ex 2)x2 3)y 4)x 5)ey

A: To find an integrating factor for the DE dy+ydx=e3x dx

Q: 3. Find (6-+- vē)dt Vy 4. Find S- dy (4-yの?

A:

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

A:

Q: Suppose that a point is moving along the path xy= 1 so that dy/dt=4. Find dx/dt when x=3.  dx/dt=?

A:

Q: If sin(x) f(x)= 68+t2 dt Jtan(x) and g(y)= f(x) dx , Then g) is equal to

A:

Q: If x^2 + y^2 = 25 and dx/dt = -2, then what is dy/dt when x =3 and y = -4

A: Given that  x2 + y2 = 25   .... (1) dx/dt = - 2 To find dy/dt when x =3, y = - 4

Q: suppose y = √(3x + 1), where x and y are both functions of t. If dx/dt = 2, find dy/dt when x=5

A:

Q: Find the particular antiderivative of the function f(x) point (0, –1). e" (2ª – 1) whose graph…

A:

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: The integrating factor of the DE   y(2x - y + 1) dx + x(3x - 4y + 3) dy = 0 is

A:

Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

A:

Q: dy 4. Let ry = 1 and dt da Find when x dt = 2.

A: By using derivative of function

Q: (a) A beam is fixed at its left end x = 0 but is simply sup- ported at the other end x = L. Show…

A:

Q: Suppose that x=x(t) and y=y(t) are both functions of t. If x2 + y2 =17, and dx/dt=2 when x=4 and…

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Q: 5x + 6x + 2. If Ax = 0.2 at x = 1, Let y = approximation to estimate Ay use linear Ay =

A:

Q: The integrating factor of the linear DE of order one + y csc x = sin x is dx

A:

Q: F(x, y, z) = (6x° sin(y) + cos(18z), xº cos(y), – 18x sin(18z) + 6z°)

A:

Q: A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?

A: We have, a particle moves on the graph of a function given as y2=x+1 Differentiating both of the…

Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: dy 4 – 5y = e-3t sin(4t) ; y (0) = 3, y (0) = 10 dy %3D - dt?

A: We solve the given IVP  y"-4y'-5y=e-3tsin(4t)........(1) y(0)=3, y'(0)=10.......(2)

Q: Find dydx? for f(x, y) = eXy

A:

Q: Suppose w = x³yz + xy +z+3 and x = 3 cost, y = 3 sint, z = 2t. Then dw dt t= . [Show solution.] =

A: Given :w=x3yz+xy+z+3x=3costy=3sintz=2t

Q: fy = f(r), how do we define the differential dy

A:

Q: Suppose that x=x(t) and y=y(t) are both functions of t. If y=2x2−1, and dx/dt=5 when x=14, what is…

A:

Q: The integrating factor of the equation 2y (x + y+ 2) dx + (y: – x: – 4x – 1) dy = 0 is: %3D

A:

Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

A:

Q: ,dz Find ifz = xy2 +x²y, y = ln x - dt

A: We are given : z=xy2+x2y and y=ln x⇒z=x(ln x)2+x2 ln x

Q: Find fr and fy- f (x, y) = 4etlo dt f#(x, y) f„(x, y) =|

A:

Q: 8. Find a continuous solution satisfying dy dr + 2xy = f(x) where = x if 0 < x < 1 0 if x ≥ 1 off…

A: Solve the following

Q: 4x + 2x + 3. If Ax 0.1 at x = 5, use Let y = linear approximation to estimate Ay Ay 2

A: A detailed solution is given below

Q: (b) YOUR TURN 4 Find dx. Vx f(x) deriv for in

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Q: Let f(x, y) = 3e" sin(5y) af af dy

A:

Q: The integrating factor of the given DE are already given below. What is the value of "n"…

A:

Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

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Q: The integrating factor of the equation (2 + y + x) dx + xydy = 0 is

A:

Q: Find the general solution using Integrating Factors Found by Inspection y(x^2 y^2 – 1)dx+ x(x^2 y^2…

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Q: 1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

A:

Q: So Sty dx dy √y(1+x²) The value of integration is very high

A: Given ∫01∫y1dxdyy(1+x2)

Q: Find dz/ðx , dz/ðy at the point (1,1,1) if x³ + z² + ye + xz cos y = 0

A:

Q: If y = 2x³ +5 and dx = 3 then find dt dy when X = -2 dt

A: Given  y=2x3+5dxdt=3 To find dydt, when x=-2

Q: What is the integrating factor of the linear De of order one ydx + (2 – xy)dy= 0 ?

A:

Q: If x3 + y3 = 9 and dx/dt = -3, then what is dy/dt when x = 1 and y = 2?

A: Given,

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

A:

Q: Find the differential dy. y =  x + 8 7x − 1

A: Assuming that y is given as:

Q: What is the integrating factor of 2ydx + x (x² ln y – 1) dy = 0 ? Oy O y?

A: Question is solved.

Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.