dy а — х— dx dy + dx а

Q: Vx 3 1- evNīdy dx - 3 y3 e*y dx dy

A:

Q: find dy/dx at the given point. (x + 2)2 − 6(2y + 3)2 = 3, (1,−1)

A: Given that  (x + 2)2 − 6(2y + 3)2 = 3 Differentiating with respect to x

Q: adx - dy 0 y dx+ +Edy = 0

A:

Q: d²y/dx²-12dy/dx+2y=0

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

Q: (y²-xy )dx + x² dy te

A: Given that, (y2 - xy)dx + x2dy = 0 We have to find the general solution of the given differential…

Q: dx Vi – 2r

A:

Q: Find dy dx and d²y dx² x = et, y = te-t

A:

Q: d/dx(arctanh(2x)) 2XIn2 A. 1-4X 2x B.- 1-4X 2 In2 C. 1+2x 2x D.- 1-2x

A:

Q: Use dy/dx = -Fx/Fy to find dy/dx. 7tan-1(x2y) = x + xy2

A: The given equation Let

Q: f cos(2-3x) cos (3x - 4)dx

A: Given integral ∫cos( 2 - 3x )cos( 3x - 4 )dx

Q: S*dx x+1)7 (x

A: Solution:To find the integral∫x2x2+132

Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

Q: 3 dy 5+ dx2 dx O degree 1 and order 3 O degree 2 and order 1 O degree 2 and order 2 O degree 3 and…

A:

Q: the following solution

A:

Q: Find dy/dx.  Y3 + (y+2)2 - 1 - x2 = x

A: Expand the left hand side expression and isolate the variables x and y.…

Q: Find dy/dx. x2 - 4y2 = 3x3y4

A: From the given data:

Q: 5x+2 find d/dx

A:

Q: 2xy +y+1 x+2xy dy dx

A: Topic:- differential equations

Q: dy/dx + 2xy + xy = 0 Ans. 1/y3 = -;+ 1 + ce3x? 2

A: The given differential equation is  dy/dx + 2xy +xy4=0

Q: T/2 V1+cosx dx T/3

A:

Q: V3x d. Evaluate dx sin(3t) dt

A:

Q: V1-x² 1–x2 dy dx -1 . J-V1-x²

A:

Q: dy dx tミ

A: dy/dx =y3/x2

Q: dx -x = ev/2 x3 dy 2)

A: By using linear differetial equation method

Q: 1 c2(1-z) Evaluate Sa-2) s(1-;-2) dy dx dz

A:

Q: Solve y = L + cosec dx

A:

Q: 24. Evalute dx r +1

A: Given: ∫0∞x12x3+1dx

Q: dy 2х dx e2y

A: Follow the procedure given below.

Q: (3x - 2y + 1) dx + (3x - 2y + 3) dy = 0.

A:

Q: (x+y+2) dy dx dz

A: The given integral is: ∫-11∫-11∫-11x+y+zdydxdz

Q: x – 1 dx x²(x + 1) “* x² – x dx x² + x + 1

A:

Q: dx 3 - cosx

A: To evaluate the integral

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.