d²y - = 0 and dx? Let y=e" +b(x+1)'. When x = 0, that dx dy a) suppose = 0. Find the possible values of a and b.

Q: If y =Aem + Be nx d'y -(m+n) dx? dy + mny = 0 dx Show that

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Q: The approximation of I = xe" dx using Simple Simpson's rule is:

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where dFdx=f(x). Simpson's…

Q: Using dy 3 =dx and dx = 0.03, what is dy whenx = 2? 2V3X – 2 dy i (Write as an exact decimal.)

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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: dx x2+y?, dt dy 2, find dt dL when x = dt If L = V -5, and 7 and y = 6. dL dt

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Q: In the case of a double integration, what changes if we change the order of integration? (Ex:…

A: we know the limits of integration the dx dy order and need to determine the limits of integration…

Q: Q1-lf x= cot-VE, y= , find dy dx' dx2 at t = 2. t+1

A: We have to find first order and second order derivative of the given parametric functions.

Q: dy Find the value of at t = 1 if dx? Vt2 + t, y = t2 + 3 x = 4

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Q: EXAM Q1-If x= cot- VE, y =;, find dy dzy dx' dx2 at t = 2. t+1

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Q: dy if x cosy =x+y. Hence find the value of dx dy if x = 0. dx 4. Find

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Q: Find dy/dx and d2y/dx2 without eliminating the parameter. x=1-t^(2), y=1+t

A: x=1-t2,  y=1+t Differentiating with respect to t, we get dxdt=0-2t  &  dydt=0+1⇒dxdt=-2t  &…

Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

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Q: dy is : If x- y 0, then %3D dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the value(s) of dy/dx  at y=1 given that x2y + y2 = 5.

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Q: Solve dy dy +y = 2sin(3x) dx? dx using the method of undetermined coefficient.

A: Given that,d2ydx2-dydx+y=2sin3x We need to find the solution of the given differential equation…

Q: Given dy dy +2- dx + 5y = e and y(0) = 0 and = 0 find the value of y(0.1) and y'(0.1) using the %3D…

A: Hi! You have posted multiple questions. As per norms, we will be solving only one question. We will…

Q: - 16y? – 16x – 16y = 0. dy at the point (3, dx ves to calculate

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Q: EXAM Q1-If x= cot-1 VE, y =,-. find dy d2y dx' dx2 at t = 2.

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

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Q: Find dy/dx in terms of t if x = te', y = 4t + 4e* dy/dx =

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Q: QA1 (a) Given that y = (3+4x²)° +10sin(5x) determine dx dy

A: The solution is given below  Please post separately

Q: If y = In(2x+3) , then find dy at x = 0. dx

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Q: sin(x+y)=xy  what is dy/dx?

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Q: Find dy du du dx dy when y and u are defined as follows. dx u = 3x - 9x² and y = √u

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Q: Given that x cos y + y cos x = 1, find dy/dx.

A: Given that, xcosy+ycosx=1. The objective is to find the implicit differentiation of xcosy+ycosx=1…

Q: Find dy/dx in terms of t if x = te', y = -5t – 5e dy/dx = [

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Q: -If x= cot- VE, y = ;, find dy dx'dx2 at t = 2.

A: We will use the formula (f(g(x))' = f'(g(x))g'(x)uv' = vu'-uv'v2 Given x = cot-1ty = 1t+1 Then dxdt…

Q: dy if y = vt' -e' and x = dx Determine In(6t)

A: dy/dx = [7/2 t^5/2 - e^t] [ln(6t)]^2/ t^2 [3ln (6t) -1]

Q: dy Find the (explicit) solution for the IVP = x + e*, y(0) = 2. dx

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Q: Given x = 8 In(t) and y = 64 t² then find dy %3| dx d²y %3D dx? ||

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Q: dy If y = (In x) (sin x), then dx

A: y=ln x(sin x) To find dydx

Q: Find the value(s) of dy at y=1 given that x²y+y² =5. dx only only D

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Q: Find dy/dx at the given point without first solving for y. xy2 = 343 at (7, 7) dy %3D dx

A: Given query is to find the derivative of the expression.

Q: Find the value(s) of dx at y=1 given that x²y+ y² = 5.

A: Given,        x2y+y2=5  and dydx at y=1

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

A: We have to find dy/dx .

Q: Q20// when x3+y3+x?y xy2+x3 dy %3D dx find the general solution?

A: Given differential equation is  dydx=x3+y3+x2yxy2+x3 the given differential equation is homogenous .

Q: dy dy if x cos 'y= x+y. Hence find the value of dx if x = 0. dx 4. Find

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Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

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Q: Q1-If x= cot- VE, y =, find 2 dy dy dx'dx at t = 2. t+1

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Q: 30. cos(r + y?) dx dy 32. x²+ y² dx dy 2 y

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Q: Find the value(s) of dx at y= 1 given that x²y+y² = 5. only В only 2

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

A: We can find the required answer as below

Q: Solve the differential equation listed below:

A: Separate the variables.

Q: dy Find the solution to dx 5xy which passes through the point (0, e). (In y)? y =

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Q: Find dy/dx if y = J' V1 + ² dt. Explain the main steps in your calculation.

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Q: Given that y = ln |2² – 6 , dy 6, find dx In |x %3D

A: Differentiation is the process of determining the derivative of the function The given function is…

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: Find dy/dx at the given point without first solving for y x2 + 3xy + 11 = 0 at (1, –4) %3D dx II

A: Given: The curve is x2+3xy+11=0 and the point is  1,-4. The objective is to find dydx at the given…