Sketch the slope field for dy/dt = y sin t for −2π ≤ t ≤ 2π, −2 ≤ y ≤ 2.

Q: Use Laplace transforms to solve the initial-value problem j – 9y = f(t), y(0) = 2, ý(0) = 0, where…

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Q: Give xy+x^2 y=2 such that dx/dt=2 in/sec. FInd dy/dt for x=1

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Q: If z = xy + 3xy', where x = sin 2t and y = cos t, find dz/dt when t = 0.

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Q: dy = et. dt Find the solution when y(0)=2 using the method of Laplace transform

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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=?

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Q: 20 dv on the interval [0, 20] dt du dt 20

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Q: By using Laplace transform to solve y" + 4y + 8y = sint with y (0) = 1 and y' (0) = 0, what would be…

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

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Q: Assume that x=x(t) and y=y(t). Let y=x^2+2 and dx/dt=2 when x=5. Find dy/dt when x=5

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Q: y" + y' = t; y(0) = 1 , y'(0) = -2

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Q: Suppose that a = x(t) and y = y(t) are both functions of t. If y + xy – 3x = 23, and dy/dt = 1 when…

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Q: Assume that y is a continuously differentiable furction in t Evaluate a) tP (+),A (+)) d tant sect…

A: Given: y is a continuously differentiable function in t. (a) To find: ∫xexπy(t)y'(t)dt

Q: Let w = x^2e^2y cos 3z. Find the value of dw/ dt at the point (1, ln 2, 0) on the curve x = cos t, y…

A: Given  By chain rule of differentiation , we have

Q: Use the Laplace transform to solve the given initial-value problem. dy — у %3D 1, у(0) %3D 0 dt

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Q: Evaluate the line integral / (7x + 5y)dx + (3x – 9y)dy along the - curve C: x =2 cos t, y = 4 sin t…

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Q: Give the Laplace transform of the solution to y' + 3y-4 e* – 2 sin(2 x), y(0)=5]

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: integral f t^3 In t dt

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Q: find the linearization at x = a: y = ex ln x, a = 1

A: fx=ex lnx,  a=1 Differentiating with respect to x, we get f'x=dexdx·lnx+dlnxdx·ex=ex lnx+1xex Now,…

Q: given xy+x2y=2 such that dx/dt=2 in/sec. Find dy/dt for x=1

A: Consider the equation and

Q: Solve by Laplace transforms. y – 3 | y(T)dr = 4e' sin(2t). %3D 0,

A: by Applying Laplace transformation and inverse Laplace transformation we get the answer

Q: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: Use the Laplace transform to solve the given initial-value problem. dy -- y = 1, y(0) = 0 dt (Đ) =…

A: Given differential equation is dydt - y = 1,  y(0) = 0

Q: Sketch the slope field for dy dt = t y for −2 ≤ t ≤ 2, −2 ≤ y ≤ 2.

A: Sketch the slope field:  dydt=ty for -2≤t≤2, -2≤y≤2. Construct the table of Values. t y dydt 0…

Q: Solve the following simultaneous DE using Laplace transforms. 2 dy fut dx 5 sin t = 0 dt −y+x+ dt dy…

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Q: (b) Use the total differential dz to approximate Az. dz = X

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Q: a) Solve the initial value problem using Laplace transform TM UTM® y' + 2y = 26 sin 3t, y(0) = 3.…

A: The differential equation is given as y'+2y=26 sin3t and the initial condition is y(0)=3 Use the…

Q: Find dw/ dt at t = 1 if w = xey + y sin z - cos z, x = 2sqrt(t), y = t - 1 + ln t, and z = pt.

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Q: compute CF d? for the veder field. KI+x3 xy> where Cis the line segment from CO.0) to Clo3)

A: The objective here is to calculate the integral: ∫CF→⋅dr→; Where F→=1+x2,xy2 And C is the line…

Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: Find dw/ dt at t = 0 if w = sin (xy + p), x = et, ln (t + 1).

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Q: at and ду ду Suppose that 3x - 4y = t and y =t sin 0. Find dt

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Q: Assume that x=x(t) and y=y(t). Let y=x2+3 and dx/dt=4 when x=5.Find dy/dt when x=5.

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Q: use the laplace transform to solve y'' + 9y = cos3t, y(0) = 4,  y'(0) = 2

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Q: Sketch the slope field for dy/dt=y2-4. How do the solutions behave as t approaches infinity? Is end…

A: Given differential equation dy/dt=y2-4. Sketch of the given differential equation is shown below :

Q: Take the Laplace Transform of the IVP (dy/dt) - y = 2cos(kt), y(0)=−9

A: Since in a given IVP it is mention that ''take the Laplace Transform'', therefore, we take only the…

Q: Suppose w = In(8x² + 2y² + 3z²) , x = 9 cos(t) , y = 9 sin(t) , and z = 8/t. Compute dw/dt in two…

A: To find: The derivative of w and the value of dwdtt=8  Given: Suppose w=ln8x2+2y2+3z2, x=9cost,…

Q: dy/dt = (y+1/2)(y+t) Use a slope field to explain why the solution that passes through (0,1) is…

A: A slope field is used to determine the approximate slope of the tangent at a point to the curve…

Q: Use the Laplace transform to solve the initial-value problem y' + 3y = 13 sin2t, y(0) = 6

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Q: Q3) by using Inverse Laplace transformation find the solotion of the differential equation y" + 9y'…

A: We have to find the solution of given differential equation  using inverse Laplace transform.…

Q: Use the Laplace transform to solve the given initial-value problem. dy -y = 1, y(0) = 0 dt y(t) =…

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Q: a) Use the method of Laplace transform to solve dx 10, dt given that x(0) = 4.

A: Since both the questions are different. So as per our guidelines, we are supposed to solve only…

Q: Use computer software to obtain a direction field for the given differential equ y' = x (a) y(0) = 0

A: Given the differential equation is            y'=x

Q: Assume x and y are functions of t. Evaluate DY/DT for 4xy-4x + 6y^3 = -258, with the conditions…

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Q: Find the intergral of  (t^2 sin(t)cos(t) +t sin^2 (t) )dt

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Q: Use the Laplace transform to solve the initial value problem. y''+ 36y = sin(6t), y(0) = 1, y'(0) =…

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Q: 4x Find the gradient field F = Vo for the potential function p == y F =

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Q: Use the Laplace transform to solve the given integral equation. y'(t) = 1- sin(t)- y(T)dt y(0) = 0

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Q: 3. Given the graph of x' vs x, sketch the direction field for x(t) that corresponds. dx dt

A: Use the graph to draw the direction field. Observe how the graph passes through the visible points…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.