If x = 5t +4 and y = 3t-7 , then find dy at t = 2. dx а. 1 O b. 2

Q: dy =/x y+5v xy is a Bernoulli equation dx The DE: Select one: True False

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Q: If x= sint and y = cost then 2 dx dy dt dt O 2 O -1 O 1 O O O None of these

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Q: Given x 19 In(t) and Y 361 t2 then find dy dx dy dx?

A: To find: The value of dydx and d2ydx2. Given: The values are x=19 ln t and y=361t2. Formula used:…

Q: Given æ = 11t – 10 and y = 121 sin t dy (i) dx dy (ii) dx? ||

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Q: Solve ysinley) dx +r Sintzy) +y) dy =o

A: Solution of the exact differential equation.

Q: Find dy/dx at the given point. 3x' + 4xy = 1 at (-1, –1) O a. 4/5 O b. 5/4 Ос. 1 O d. -5

A: Using  differentiation of product rule,

Q: 9. If y = sinh 4t and r = sinh t, show that 2 dy (a) (1+2²) = 16(y? +1), dr dy (b) (1+x²)- dx2 dy…

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Q: dy 5 implicitly, if e*(e – 1) + sin(2x + 5y) In(v7) - cot(2x) - = - dx y+2

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Q: Find P.I of the given d'y 5. +6y ex dx sdy dx?

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Q: find dy/dx in terms of x and y if (x-a)^4+y^4=a^4. Assume "a" is a constant dy/dx=?

A: Given: (x-a)^4+y^4=a^4

Q: find the dy/dx of the following {(x=√1-t),(y=√1+t)

A: To find: The value of dydx. Given information: x=1-t,y=1+t

Q: Find dz/dx if z is implicitly given by the equation ze-y = sin(ryz).

A: Given, zex-y=sinxyz It is simplified as follows: Differentiate both sides with respect to x and…

Q: In the given Bernoulli's equation 6y?dx – x(2x³ + y)dy = 0, what is S P-(y)dy? Iny 1/y

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Q: The solution of the DE dy + (y – 1) dx =0

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Q: Find the general solution of the given Attached equation

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Q: Given x = 4 In(t) and y = 16 t² then find dy dx d²y dx?

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Q: If z + In(e2x - e + e²) = 0 dz find at the point (0, 0) dx 2 0 -3 -2

A: see below the calculation and answer

Q: If x =t-1+5 and y 6+t-2 then dy at t = dx is

A: topic - derivatives answer is 4

Q: (a)Use the shooting method to solve: d'y dy = e*; y(0) =1; y(1) =-1. dx dx? Use h=0.1

A: Given that, d2ydx2-ydydx=ex; y(0)=1, y(1)=-1h=0.1 Here we use the Euler's formula: yn+1=yn+hf'xn,yn…

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: Solve the following DE: -y dx +(x+/xy) dy=0

A: Given  -y dx+(x-xy)dy=0

Q: choose the correct answer If y = t^2/(t^2+1) and t= √(2x+1) the dy/dx =

A: Given, y = t2t2+1   and  t = 2x+1 We have to find dydx.

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: cinxo ) 2X. dy dx Find for y= cos ( Inx + e

A: We have to find the derivative.

Q: (In x)² dx, .3 te ato u a ? and dy

A: Integratipn by parts problem

Q: y = cos s (2² + 7) dy Find dx dy dx

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Q: Given x = 2 cos t + 8 and y= 4 sint dx (i) dt dy (ii) dt dy (iii) dx ||

A: Givenx=2cost+8y=4sin2t

Q: If 3x2 +2xy +y² = 2, then the value of dy at x=1 is dx

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Q: FIND DY/DX OF THE FOLLOWING 6. y=sec'Inx

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Q: Find dy/dx at the given point. (2t + 9, 7t − 9), t = 1

A: We have to find dy/dx at the given point - (2t + 9, 7t − 9), t = 1

Q: If we solve the DE y dx + 2 x dy 0 alter converting it to Exad using an

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Q: If x t-t3 and y = t2-t, the value of at t = 2 is dy dx

A: It is simple differentiation.

Q: 4 dy 5. х dx + бу %3D 3хуз 3xy

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Q: Solve the following DE: -y dx + (x+xy) dy=0

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Q: dy The solution of dx with initia y

A: Introduction: Separation of variables: This method is only practicable if the differential equation…

Q: ery dx dy. 0.

A: ∫01∫01exydxdy Take ∫01exydxSubstitute u=yx=∫0yeuyduTake the constant out:…

Q: Zy dx = (x?-1)L dx-dy) %3D

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Q: ) dx dy is

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Q: D. Find dy/dx of the following and simplify x v4-x y= Arccos

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

Q: The general solution to the DE + Py =0 is dx

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Q: Find the solution of the this differantial equation. extan(y)dx + [(ex)/(x-1)]dy = 0

A: Hair we use the variable separable method to solve this equation.

Q: Find the solution of dy X. +y.Inx y.lny dx Show all your calculations.

A: Given equation is as below :

Q: 2. Determine y so that it will satisfy the equation: d'y_dy dx = 4e* +3e²* dx with conditions y(0) =…

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Q: хуз dx + e** ,3 dy = 0.

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Q: if y=u, u=v -1/2 and v=lnx, what is the value of dy/dx at x=e

A: Calculate the value of dy/dx and then put x=e .

Q: d’y dx? Find the general solution for +10 -+25y = 0. dx

A: For the second order homogeneous differential equations of the form ad2ydx2+bdydx+cy=0 , the general…

Q: 14. e see" y dy = dx +x dy.

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Q: 36 sin t Given x = 6t – 15 and y dy dx dy dx?

A: Explanation of the solution is given below...