y 3x+ 6 cosx, 0 £xs 2n

Q: Solve the given diffential by variations of parameters 1. y" + y = cos x

A:

Q: Find the solution of the equation a²z a²z + cos y ax² dy² which tends to zero as x→∞ and has the…

A: Given partial differential equation is ∂2z∂x2+∂2z∂y2=e−xcosy. It can be written as follows…

Q: y" + 2y' = 4x – 5 cos(x).

A:

Q: Solve the following equation using separation of variables: dy 2y- cos(x) dr 1+ sin(x)

A: Cross multiply the equation and solve

Q: I need help to find particula solution using undetermined coefficients: y''+4y = sin(t) + t2 + et

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Q: y" + 2y' = 2 – 5 cos(x), y(0) = 0, y' (0) = 1. %3D

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Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = - 400 sin(2t) Y(t)…

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Q: Find the value of zrr at the point (0, 3, 2) where x²y? + z² – cos(xyz) = 10. |

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Q: Check by differentiation that y = 2 cos t + 6 sin t is a solution to y"+y= 0 by finding the terms in…

A: Here,  y=2cost+6sint

Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: Find the solution of the equation cos y dy? which tends to zero as x → 0o and has the value cos y…

A:

Q: Simplify (if necessary) then Compute: y" +y' for [6(cosh2x- sinh2x)] d -3x2 dx a2 y(z) = [; (z²x+…

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Q: Use undetermined coefficients to find the particular solution to y"+ 5y' + 4y = - 500 sin(3t) Y(t) =

A: We have to find the particular solution of  y''+5y'+4y=-500sin(3t) by using the method of…

Q: Find the solution of the equation = e Cos y which tends to zero as x - 0o and has the value cos y…

A:

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

Q: Q3) A: Find y if: a- y = sin 2x + 2 cos x c- y = sin √x (As... b- y = secx. csc x d- y = tan(2x + 1)

A: Please see the attachment

Q: if y^3 + y = 2 cos x, find the value of d2y/dx2 at the point (0, 1).

A: Given,

Q: In the equation where y" + 4y = 0, A. Show a solution for all the values of the arbitrary constants…

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Q: Find the solution of the equation a²z a²z + cos y V ax² dy² which tends to zero as x→∞ and has the…

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Q: Show that y / / + y = 0 given that y = 2 sin x + 3 cosx

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Q: y = sin(Ax + B)

A: We will find the Differential equation as following.

Q: Let I = 3x*cos (x) dx. The approximation of / using the two- formula is:

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Q: Find all intersection points between r = –sin 0 and r = v = V3 cos e.

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Q: (b) Find, where y= cos ecx- dx -4x+7

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Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i и

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Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

A:

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find fx(8,9,0). Leave your answer correct to two decimal…

A: Solution

Q: dz Find a? sin(2y – 5z) =1+y cos(6zx)

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Q: cos 2y dy sin y

A:

Q: A particle moves in the xy-plane so that its position at any time t is given by x= cos(5t) and y =…

A: According to the questionx=cos5ty=t3

Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: satisfied

A: We will solve the problem.

Q: check by differentiation that y=5COSE 4 Sint is a solution to y"ty=D0 by finding the terms in the…

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Q: Find y' and y". y = cos(x?) y' - -sin (x²) ( 2x) y" =

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Q: Find the solution. dy sin x x +2y = y(2) = 1 dx , X A y = (4 + sin 2 + cosx²)/x² (B) cy= (3 cos 2x -…

A:

Q: у" + 4y' + Зу %3D sin (e*)

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Q: Given f(x,y,z) = cos(5xy) + sin(4z). Find fx(6,6,0). Leave your answer correct to two decimal…

A: Given f(x,y,z) = cos(5xy) + sin(42). Find fx(6,6,0)

Q: ) Solve to find if y = sinvt – t, and t = cos (2x) – secx dx

A: Given: y=sint-tt=cos(2x)-secx To find: dydx

Q: Integrate x cos(2x^2+7) dx. Select the correct response: O sin (2x^2+ 7) + C

A: Integrate using substitution method.

Q: Obtain the der a) cos(xy)=2y, find y'

A:

Q: 3) Show that y" +y = 0, given that y = 2 sin x + 3 cosx

A:

Q: Find the solution where y= 1 and dy/dx = 0 when x =0 and describe the behaviour of the solution for…

A:

Q: 3.) Solve the equation using discontinuous function: y" + 9y = cos(2t) – U37(t)cos(2t) , y(0) = 0,…

A: We will find out the required solution.

Q: Find y" at (2,4) for cos(x²y + 5) = 16. %3D

A:

Q: Find the solution of the equation = e Cos y which tends to zero as x → 0o and has the value cos y…

A:

Q: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy?

A: Partial derivative of a function of two or more variables with respect to one variable is the…

Q: Find the solution of the equation =e COs y %3D hich tends to zero as x 0o and has the value cos y…

A:

Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

A: Solution is given below

Q: Solve the fo llowing D.- E y + y tan X Cos X %3D

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.