For x=e2 y=In 2t. find y' when x=e. O 4e e 4e O e -|

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: Q22. If y=tan x+ tan dy is: -then dx 2 (d) 1+x (a) 0 (b) 1

A: Given function is                                          y=tan-1x+tan-11x we have to find…

Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

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Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

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Q: So lve the di fferential equation dy + y - ecos x = 0,0 s x s0.5, y (0) = 0 by (a) Milne's me thod…

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Q: Solve D.E using Exact from first order 2.xy dx +(x² +3y²)dy

A: To solve the given differential equation.

Q: 2) Obtain the DE with respect to x of (x - h)² = 4(y-k).

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Q: Let y 5x? + 5x + 2. || Find the differential dy when x = 5 and dx = 0.3 Find the differential dy…

A: GIVEN: y = 5x2 + 5x + 2

Q: Solve (1+x ) = x²y, given that x=1 when y = 2 dx Find the particular solution for y in terms of x.…

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Q: 3. ex In y dy – y e` dr = 0 2 (In y) In y + e* = c In y - e+1 2 (In y)- e* = c

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Q: Let y 4 Find the change in y, Ay when ax = 0.2 4 and Ar Find the differential dy when 4 and da 0.2 =

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Q: A. Find dy/dx of the following. 1. y = e" + eVinx + 2 In(ex) 2. y = er" 3. eln 4x + eln 4y = e + e"

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Q: Let y = 4/T. Find the change in y, Ay when a 3 and Ar Find the differential dy when x 3 and dx 0.2

A: fx=4x here x=3 f3=43 . Δx=0.2 fx+Δx=4x+Δx f3+0.2=43+0.2 f3.2=43.2 . Δy=f3.2-f3 Δy=43.2-43…

Q: if x²+y²=t-- and x*+y*=t*+=,prove dy X t dx 3. ху

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Q: Find dy/dxin terms of x and y if (x−a)^4+y^4=a^4. Assume that a is a constant. dy/dx=   implicit…

A: (x−a)4 +y4 =a4 a is a constant. dy/dx = ?

Q: (b) Given that y(6x +1) e** = 1+ - In dy Find when x 0 and y=1. dx

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Q: 3. Determine the Particular solution of this equation In terms ofY (xy2)dx + e*dy 0, as x → 0, y ==

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Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

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Q: If z = cos x - e¹, x = 1² + 1 and y = 5 + ln t, then equals: dz dt

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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: if x² + y² =t -- and x* + y* = t dy prove dx 1

A: Given, if  x2+y2=t-1t and  x4+y4=t2+1t2 To prove that  dydx=1x3y

Q: (ylny - e¯xy)dx + ( + x lny) dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact differential equation. If it satisfies the…

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: Let y = e"/1. Find the differential dy when x =1 and dæ 0.2 Find the differential dy when a = 1 and…

A: This question is related to differentiation. We will use basic differentiation results to solve this…

Q: Let y = e/3 Find the differential dy when x = 5 and dx 0.2 Find the differential dy when x 5 and dx…

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Q: If f(x) = – x Find: S",(f(x))² dx That is find S"(: ,(1 - x)?

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Q: Suppose y = (x² + 5)³. (a) Find the differential: dy dx. (b) Compute the differential when x dx 2…

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Q: Let y = tan(3x + 7). Find the differential dy when a = 4 and dæ = 0.3 Find the differential dy when…

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Q: (4 + e² ë*) dx + (1 +et) dy.so *) dy so A Scanned with

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Q: dy dx || X x² + 100

A: We have given differential equation  dydx=xx2+100 dy=xx2+100dx Integrating both sides…

Q: Find the change in y, Ay when x = 4 and Ax = 0.4 Find the differential dy when x = 4 and dæ = 0.4

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Q: Use Euler's method to estimate y(0.02) ey-x y' = 1+e3y „y(0) = 4 0.01) What is the error in the…

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Q: 2. 2メ dy dx for y = Cos (ln x + e put lに

A: y = cos2(ln(x) + e2x)

Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y (0) = 3

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Q: Find the general solution to dw ol Sa'(t) = x(t) – y(t) + 3e'; ly'(t) = y(t) – x(t) + 2e'; (8) (8)…

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Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

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Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y ( 0) = 3

A: We can solve the given differential equation by using initial condition.

Q: dy 13. y(1) = e de ar(In y - Inr + 1)'

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

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Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

Q: 56. Given that x+y - xy and that y dx dy when x 1 show that xy = e*

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the general solution to the following DE. y +x² dy = 0 dx

A: Given DE, y2+x2dydx=0

Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: Use Euler's method to estimate y(0.02) ey-x y' 1+ e2y »y(0) = 1 (h=0.01) .What is the error in the…

A: The solution is given as