13. x'y 3 + x³y5 = Ċ %3D

Q: -- with initial conditions y(0) = 1, (0) =

A:

Q: 7. Evaluate Soy4 2 - y dy using Gamma/Beta function.

A: The solution is given as

Q: Express the solutions of the initial value problems in terms of integrals. dy/dx = sec x, y(2) = 3

A: dydx   = Sec xdy  = Sec x dx Integrate both side

Q: 16. Suppose the radius r, height h, and volume V of a dh related to dt dV cylinder are functions of…

A: Given: A cylinder with radius, r and height, h. The formula for the volume (V) of the cylinder is…

Q: Solve the initial value problem. dy 3 dx - = x˚ (y - 5), y(0) = 9

A:

Q: 3. What is the difference between a solution of a differentialequation and a solution of an…

A: The solution represents a family of solutions all of which satisfy the system of differential…

Q: Find the Differential Equation of the following family of curves 4. Straight lines with slope half…

A: The equation of straing line is given byy=mx+cwhere,m=slope=dydxand, c=y-interceptat…

Q: Problem 2.3 i. and 2.3 ii

A: Given initial problems are

Q: 1. Find the rate of y with respect to x at the point (5, 8) if 7y-ry 4. dy da

A:

Q: 28. Differentiate implicitly to find dy/dx if x + x/y = 7.

A: Given, x3+x/y=7 we can also write as yx3+x=7y,  or y=x7-x3 derivate both side w.r.t x…

Q: dy 4. Solve the initial value problem : (1+x²). -= yx, y(1) = 2 dx

A: The given differential equation is 1+x2dydx=yx, y1=2.

Q: Inx Iny mz dx dy dz

A: Given integration is  I=∫1e∫1e∫1elnxlnylnz dx dy dz=∫1e∫1e∫1elnx dxlnylnz dy dz…

Q: Suppose that glucose enters the bloodstream at the constant rate of r grams per minute while it is…

A:

Q: Solve the initial value problem. 2x* - х - 4 2 dy X dx (x+1)(у+1) y(1) = 3

A:

Q: What integral equation is equivalent to the initial value problem y′ = ƒ(x), y(x0) = y0?

A: Write y'= dy/dxThen separate the variables.

Q: 1 1 LGt-5- At²est + Ceisinh Dt = [(s – 1)3 ' s² + 2s – 5]

A:

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: 2. (1+Inx)dx +(1+Iny)dy = 0 when y( - 2) = - 1.

A:

Q: 2 1 Estimate -dx using the right endpoint rule with n = 4 3 1+x

A:

Q: Which óf thé fóllówing directión fiéld will represent the differential equation y' = y + 1 Option 1…

A: Direction field: A graphical representation of solutions of a first order differential equation is…

Q: Differentiate. y =x° In x- dy II

A:

Q: 4. If a point is moving along y = 3x2- 4x – 6 at a rate of = 4 m/s, find dt when x = 3.

A:

Q: y ln x - x ln y = 1

A: ylnx-xlny=1Treat y as yx

Q: IPydx dy 20.

A: To evaluate: ∫02∫13 x3y dxdy

Q: 2 Solvehe initial value problems below. dy dt

A: The general solution of a differential equation always contains a constant of integration. The…

Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: solve the Initial Value Problem using Separation of Variables. y' = xy2, y(1) = 2

A:

Q: Find dy/dxin terms of x and y if ax^4−by^4=c^4 Assume that a, b and c are constants. dydx=…

A: Given : ax4-by4 = c4 a, b and c are constants. To determine dydx

Q: Cln S iny 7. ex+y dx dy 0.

A: I=∫1ln8∫0lnyex+ydxdy⇒I        =∫1ln8ey∫0lnyexdxdy               =∫1ln8eyex0lnydy…

Q: dy 3. y = [(x + 1)(x – 1)]³, dx dy 4. y = (t + 4)(t – 2)(t – 1), dt 12/07/2021 15:

A:

Q: 6) Calculate - dx for z = ln(x + y²).

A:

Q: 5. The integrating factor of the di equation 2y dx + (x- x^3 y^3) O x*3 y^2 O Does not exist

A:

Q: 4. S 2z3 el-z dz 5. S Vx In(Vx) dx Vr3 6. Si, Inx dx

A:

Q: -5 1 -dx Jo 2x+4 1 dt 2 V6-t 1 ii) S,

A:

Q: Soru 1. (1+ 25)dx + 20* (1 - )dy = 0 ; -) dy = 0 ; + 2ey) dx y(0) = 1,

A: Given that:                           1+2exydx+2exy1-xydy=0    .........................(1)…

Q: 5) Inx Iny mz dx dy dz

A: Given: Let I=∫1e∫1e∫1eln x ln y ln z dxdydz To Find: To evaluate the given integration

Q: 2) Integrate: S(29sinx + 6e + 5 cos x + Vx)dx

A: Given that, The integral ∫29 sinx +6ex +5 cosx+x5 dx By using ∫f(x)+g(x)dx =∫f(x) dx +∫g(x) dx ∫ 29…

Q: ion dy 3t2 dt 2y + 2t3y' tion: ||

A:

Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: cln 4 cln 3 cln 2 10. Compute e0.5x+y-z dz dy dx.

A: Evaluate the integral: ∫0ln4∫0ln 3∫0ln 2e0.5x+y-zdzdydx=∫0ln4∫0ln 3ey+0.5x∫0ln2e-zdzdydx=∫0ln4∫0ln…

Q: بال 20 S 3y م + dx dy

A: The double quintessential is maximum typically used to calculate the floor vicinity of a…

Q: 2-S S dx dy

A: to find the double integral we consider a strip parallel to x axis

Q: Find explict solution of the foilowing initial-value problem dy yoanx?, yla)of %3D dx

A:

Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

A:

Q: Solve the initial value problem dy y = 5e" + 28e5* dx with y(0) = 8.

A: The solution of differential equation is given as follows :

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.