4. y"+2y'+2y=e* cos x 3t 2.x"-2x'–4x = 2e" 27 6. x"-4x'+4x= te" %3D 5.

Q: 3x4-4 cos x = -6

A: Find d2y/dx2 implicitly in terms of x and y3xy − 4 cos x = −6

Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

Q: y"" - y' = 2e-* - 3e2x when x = 0, y = 1, y'= -1 and y" = 2

A:

Q: y"1 +y1 = 0. У 2- У2 %3D 0.

A:

Q: y"" 1 x² ln x

A: As per our guideline, we are supposed to solve only one question. Kindly repost other question as…

Q: 13. Find mzEDC. (9x- 1)° EE C. A (2r + 13) D

A:

Q: 7. Let y = tan (3x - 2), find y'.

A:

Q: 7. y = cos`x sin'x %3D 3 A. – 4 cos x sin x B. – 2 sin sin 2x 3 2 C.- 4 cos´x + sin' D.- 2 sinx cos…

A:

Q: solve the following DE X^4 y' + 66x^3 y = x ^-2 cosx

A: The given differential equation is  x4y'+66x3y=x-2cosx.   The by parts formula of integration is…

Q: n/3 sec23x 8. n/4 2+4tan 3x dx

A:

Q: (x²y* + 2xy)dx + (2x³y³ – x²)dy = 0 -

A:

Q: Ex6: Solve the following 1. If x? + y² = 25 show that (y')² + yy" + 1 = 0 2. If xy = sin x show that…

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

Q: 1. Calculate an expression for = y if V+b°y = tan-(x"y)

A:

Q: Find y' if 4 cos x cos y = 3y. %3D

A: To find the derivative.

Q: 8. (x² + 2xy − 4y²) dx — (x² − 8xy — 4y²) dy = 0. - -

A: #8

Q: Q.34. (CotX cosX)/(TT-2x)^3 equals (1) 1/24 (2) 1/16 (3) 1/8 (4) 1/4

A:

Q: Evaluate y” - y’-2y = sin2x

A: Using method of linear differential equation.

Q: y"+y=sec³x

A: The given equation is: y"+y=sec3x

Q: y-y-coshx Ans.

A:

Q: (3– 3cos5x)} (3x² +2x-7)² (e - sinx +3x) y= Find dy/dx if

A: That's computational, take a careful look.

Q: find a linear homogenous constant coefficient equation with the given solution: y(x) =…

A:

Q: 5. (y" – y) = e-X cos(3x) %3D

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

Q: 9. Evaluate y' of y = e-2*sin3x a. 3e-cos3x- 2y b. 3e-cos3x- 3y c. 3ecos3x - y d. 3e-cos3x +y e. Not…

A: Explanation of the answer is as follows

Q: b. fx'e*** dx 2sinx C. 3+cosx c. S; S5x* dx a. dx 7x2

A:

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

A:

Q: Can we write the general solution of the equation y" + (1/x)y' + (1-1/4x^2)y=0 (x#0) for its two…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.