2 tan-1(y). x In(xyz), q ƏV when x = y = % = 1. ду Let V = eP cos(qr), with p = z cos(TY) and r = By using the chain rule, find

Q: 4) The vertical displacement of a spring mass system from its natural length is described by d²y dy…

A:

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: y=Ae5x+Be6x

Q: Find the differential dy for the given values of x and Δ x. y = 5x 2 - 2x + 3 ;  x = 2 , Δ x = - 1…

A: Given that: y=5x2-2x+3,  x=2  ,  Δx=-16

Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

A:

Q: дт ду д dy at az az & as Calculate by first finding & and using the chain rule. at as' as' at

A: Follow the procedure given below.

Q: Given a function : E = 1/2 mv^2 + 1/2 kx^2 Where, x = A cos(wt) v = dx/dt k= mw^2 A, w are constants…

A: Given information: The function is E=12mv2+12kx2, and the value of x=A cos(wt), v=dxdt and k=mw2. To…

Q: 1. If z = 2xy – 3x²y and x is increasing at 2 cm/sec determine at what rate y must be changing in…

A: Z is neither increasing nor decreasing at the given instant. A function is said to be neither…

Q: Find dy/dt if y=ln(t^2+1)/(squareroot of (4-t)

A:

Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

A:

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

A:

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: Choose the correct steady-state oscillation of y" + cy' + y = r(t) with C>0 and r(t) = sin(4t) . 4c…

A:

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

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

A:

Q: Find the differential dy of the given function. y = InV9 - x2 dy =

A:

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

A:

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

A:

Q: () 2. If k = w3 – wv², w=xy, v = w+ x, find and using: dw a) the chain rule b) differentials.

A: Given: k=w3-wv2, w=xy, v=w+x   To find: (∂k∂w)x . (∂k∂x)w  using chain rule and differentials

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 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: 7. Find the differential dy for y = x2 – 4x + 6, then evaluate it when x = 2 and dx = 0.1 -

A:

Q: S(«,9) =7+3y Also, find the total differential of the function.

A:

Q: (b) Find the general solútion of the differential equation d'y dy 2 +y x+1 dx - dx2 without using…

A:

Q: dy 1; find dt dx at x =- dt Related Rates: Given y = cOs x + sin and 4

A:

Q: х+1 y 2x 1

A: Given,            y = x + 12x - 1

Q: T. Selue the ff. differential epnotion ) xy (xdy tydy) = ky'dy; when yol; x=2

A:

Q: 5. z = yex+x Iny xey-y lnx

A:

Q: 4) (2x + y cos xy) dx t x cOs xy dy - o cOs xy) dx t X COS Xy dy COS

A:

Q: I Example 10.24. If = dy 2eły, y(0) = 2, find y(4) using Adams predictor corrector for- dx mula by…

A: here we need to use Adams predictor-corrector method and Euler's modified formula.

Q: Consider P(D)y = 0. What conditions on the rootsof the auxiliary equation would guarantee that…

A: Solution: Consider the given Differential Equation P(D)y = 0 Let the Auxiliary Equation of given DE…

Q: 4) The vertical displacement of a spring mass system from its natural length is described by dy…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: 1. How many stable equilibria does the following autonomous differential e y' = y³ + 4y² + 4y

A:

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

A:

Q: Let y = 3x². Find the change in y, Ay Ay when x when x = = 5 and Ax = 0.3 Find the differential dy…

A: Given f(x)= 3x2

Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

A:

Q: y = 3 Arccos ( 1 -)+ v6x – x² y= In (*+1), (x+2)3 x²(x+1), e2x-e-2x y = e2x+e-2x

A:

Q: Let y = 4ĩ. Find the change in y, Ay when x = 4 and Ax = 0.3 Find the differential dy when x = 4 and…

A:

Q: Let y=3x^2  Find the change in y, Δy when x=5 and Δx=0.1    Find the differential dy when x=5 and…

A:

Q: z = xey + y ex

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Compute the differential dz of the function. 6.7 Z = x dz ||

A: Here, to find the differential dz of the function z=x6y7 Note that: dz=zxdx+zydy...(1)

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

A:

Q: 3. Find dy, where; (x+y) = 2 a) cos (xy)- + e b) e+ iPtany=1 , u= xlax (use chain rule)

A:

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

A:

Q: 4- Find dy/dx for y = 3(sin-(e-3x*)2 dy 31(sin-(e-3*")r* In3 2(sin-'(e-3x")- dx 1(-6х) е 1 - e-6x2

A:

Q: Let y=(x2+4)to the 4th power. Find the differential dy when x=3 and dx=0.3.... Find the…

A:

Q: dw 3. Given w=ln (x²+y) where x=2t , and y=4-t . Find in two ways: dt (a) Using the appropriate…

A: Given:- w = ln(x ^ 2 + y) where x = 2t , and y = 4 - t . To find:- dw/dt (a) Using the appropriate…