dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos a – sin xy; x = - y = 4t t' Enter the answer in terms of t. dz dt ||

Q: Show that the 2-D Heat Equation dx² ди becomes ди if x = es cos w and y = es sin w. You ma dt dy?…

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Q: Find the differential dy of the given function. y = csc 2x

A: Consider the function

Q: b) Use the Laplace Transform to solve the following differential equation given the initial…

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Q: Solve the differential equation using Laplace Transform and Inverse Laplace transform y" – 4y' + 4y…

A: The given problem is to find the solution of differential equation using Laplace transform with…

Q: 14. Solve the equation d?x 3 +2x sin dt2 dt dx given that at t = 0, x = 0 and 1. dt nent

A: See the details solution in below

Q: Find the differential dy of the given function.

A: Here we will Compute the first derivative dydx  And the rule we will use for computing is known as…

Q: D. Solve the differential equation using Laplace transform of y - 3y' + 2y = et ; when y(0) =0 and…

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Q: The order and degree of the partial differential equation respectively 6 9. dz + sin x = xy? is_ %3D

A: Given,          ∂4z∂x46+∂z∂x9+sinx=xy2

Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: Q1-Use the chain rule to express dy / dx in terms of xand y: 1-1 a) y = аnd x = at 1= 2 1+1 b) y=1-…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

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Q: Solve the differential equation using Laplace transform of y" − 3y' + 2y = e3t ; when y(0) = 0 and…

A: Given differential equation is  y"-3y'+2y=e3t,  y(0)=0 and y'(0)=0

Q: Q:- solve the differential equation by Laplace transform : y" – 3y' + 2y = e3t %3D Where the initial…

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Q: d3x 2. Verify that sin kt is a solution of the equation in + k3x = 0 %3D dt3

A: Explanation of the answer is as follows

Q: 6) Use Laplace transforms to solve the differential equation: dy dx2 dy -7- ·+10y=e2* +20, given…

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Q: 4. Given y = 3u² – u and u = x³ – 1, use the Chain Rule in Leibniz notation to find the value of dy…

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Q: Solve the differential equation by using Laplace Transform y''+4y'=15et y(0)=5,y'(0)=-2

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Q: Find the differential dy of the given function: y=sin2x-4x

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Q: Use Laplace transforms to solve the differential equation de +4-+ 40 = sin (8t) dt d? given that 0…

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Q: Let y = 5x?. Find the change in y, Ay when a = 3 and Ax = 0.3 Find the differential dy when x = 3…

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Q: Find the differential dy of the given function y = csc 7x Jax dy :

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Q: A particle moves on the circle x2+y2=25 in the xy-plane for time t≥0. At the time when the particle…

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Q: y" – y' – 2y = sin 3t y(0) = 1 and y'(0) =-1

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Q: Hello! Can you help me with this calculus problem?

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Q: If y(x) satisfies the differential equation y" + x²y = 0, where y(0) = yo and y'(0) = y, show that…

A: since we know that L[y''] = p2Y(s)-py(0)-y(0)

Q: Find the differential dy of the given function. y = In√√/9-x² dy =

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Q: find the integrating factor of the given linear DE and general solution of the y'+1/x (y)=cos(x)

A: Consider the given linear differential equation. y'+1xy=cosx The objective of the problem is to find…

Q: Solve the differential equation using Laplace transform of y" − 4y′ + 4y = 4 cos 2t ; when y(0) = 2…

A: Solve given differential equation by using Laplace transform. y" - 4y' +4y = 4cos2t when y(0)=2 and…

Q: Find the particular solution of (cos x – x sin x + y²) dx + 2xy dy = 0 that satisfies the initial…

A: Make the absolute form and solve this differential equation.

Q: dx +4x = 2e 3 , x(0)= 5 dt (d) dx +4x = sin 2t , x(0)= 0 dt (e)

A: Laplace transferom, solve the differential equation by using Laplace transferom

Q: Find the general solution of the differential equa- tion / - a?y = -x - xy, %3D where |r| < 1.

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Q: Find the differential dy of the given functions . (Use "dx" for dx.) a) y = 2x − (sin(x))2 b)…

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Q: dx 2а — У dt fip dt x + 2 cos(t)

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Q: dy The integrating factor of Linear differential equations + y x 4tan ¤ = sec²x is_ dx In cos 4x tan…

A: The coefficient of y is: P=4tanx So the integrating factor is: e∫Pdx

Q: Find the change in y, Ay when x 1 and Ax = 0.1 Find the differential dy when x = 1 and dx 0.1

A: Let y=5x^3

Q: y" + 9y = 5t + 2, y(0) = 2 y'(0) = -1 |

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Q: Find the differential equation such that y(x) = (x + 10)°(c,cos(2ln(x+ 10)) +c,sin(2ln(x+ 10))) d²y…

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Q: Is the function p(x, y) = sin? (xy²) a solution to the partial differential equation + (2x + y)(2y)…

A: Use 2sinxcosx=sin2x And put the given solution on both sides we get both sides are equal  And…

Q: Let y = y(t) be the solution to the initial value problem dy = e' cos t; y(0) = 1. - dt Find the…

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Q: ve the given differential equati dy dx - (1 + x)y = xy

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Q: Find the differential of the function. Z = e-9x cos(2rt) dz = dx + dt %3D

A: The total differential of the function  is given by . So, to find , first we need to find the…

Q: Given the differential equation y'' − 3y' – 4y = - 2 sin(2t), y(0) = 0, y'(0) = - = - 1 Apply the…

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Q: . Solve the differential equation dx 9 x = sinh(2t) with x(0) = 1 by using the Laplace transform.…

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: 3 a) Find the exact integer value of a for which tsin (at)dt == ft sin (xt) dt = -². where a1. T

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Q: Find the differential dy of the given function. y = x(1 − cos x)

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Q: ci. use laplace transforms to solve the inittial value problem: У' — y' – 3y = F (t), where y(0) = 0…

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Q: y"+16y = cos4t, y(0)= 0, y'(0) = 1,

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Q: THE IVP

A: Consider the provided differential equation with initial condition is,

Q: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx)  y = (2 x3 − x2…

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Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…