x = 2, x = 4, y = x - 1 y : 4 X - 1

Q: y 2. JJp x5+1 dA, D = {(x,y)|0 < x < 1,0 < y<x²}

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Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = (x + y)/(xy - 1)

A: We first find the partial derivative with respect to x. Use the quotient rule.

Q: fc y 3 ds, C :x=t2, y=2t, 0&lt;t&lt;1

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Q: a) -x +y - z = 0 2y + z = 3 z = 0

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

Q: (b) x' = -x – 3y + 2z + yz, y' = 3x – y – z + xz, z' = -2x + y – z + xy.

A: As per your query the solution of the part (b) has been done in detail in the following steps.

Q: Es, given that x(0) = -1, and y(0) = 0 *+x+2y-1=0 2x+y+y-2=0

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Q: 2. y" – 3y" + 3y' – y = x²e*, y(0) = 1, y'(0) = 2, y"(0) = 3 %3D

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Q: 3. y" – xy' – Y = 0, xo = 1 -

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Q: 1 yy" + (y)² = yy' y(0) = 1, y'(0) =

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Q: z(y" – y') – (y" – y) = 0, 1 y(0) = 1, y'(0) = 3.

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Q: y" + 4y = 0, %3D y(0) = -4, y'(0) = 6, y"(0) = –8. y(x) =

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Q: 5 y"+y'+y =t-Un/2(t) 4 y(0) = 0, y'(0) = 0 2

A: Consider the given differential equation.

Q: 27) y"+2y'+ y = e", y(0) = 0, y'(0) = 0.

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Q: 9x-y+z=3 10x-y+z=8 Find (x,y,z)

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Q: d.A, A = {(x; y) E R² : y € [0, 1], x € [y², e-]}

A: Given: I=∫∫A1x34dA   A=(x,y)∈R2: y∈0,1, x∈y2,e-y

Q: y' +y = x*y2 , y(2) = -1,x > 0 is

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Q: 19. x' = -2y, y' = 2x; x(0) = 1, y(0) = 0 %3D

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Q: y"(x)-4y'(x)+4y(x) = eax,a E R %3D

A: Given Let’s plug y'=D Hence, Auxiliary equation becomes Complimentary function will be

Q: y=xy+x-y-1, y(0)=0

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Q: 23- y" + xy = 0, y' (0) = 0, y' (L) = 0

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Q: x²y" - xy + xy = 0, y(1) = 0, y (L) = 0, L > 1

A: As per the question we are given a second order linear differential equation as : x2y'' - xy' + λy…

Q: y(3) + 9y' = 0; y(0) = 3, y'(0) = –1, y"(0) = 2; y1 = 1,

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Q: d) xty"- x'y'-(y') = 0, y(1) = 2, y'(1) = 1 %3D

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Q: {e, 9) € R² : 52. {(x,y) € R² : (y-x)(y+x) = 0} (y-x²)(y+x²) = 0}

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Q: find ƒx , ƒy  . 1. ƒ(x, y) = (2x - 3y)^3 2. ƒ(x, y) = (x3 + ( y/2))^(2/3) 3. ƒ(x, y) = x/ (x2 + y2 )

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: y' +y = x*y2 , y(2) = -1,x >0 is

A: Given, The initial value problem is,

Q: y" + y = >(-1)"5(t – 2rn), y(0) = y/(0) = 0 n=1

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Q: 4. Y= C, ex + C2e* + X

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Q: y"' + 2y" + y' = e*, y(0) = 0, y'(0) = 1, y"(0) = -1

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Q: y" + 4y' + 4y = (3 + x)e¯2x, y(0) = 2, y'(0) = 5

A: See the attachment

Q: SIL- W : x² + y} < 9, 0<z<6

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Q: // (x+ y) dA, A = {(x; y) E R² : x € [0, 1), y E [2x, 2V]}; A

A: To evaluate the given double integral

Q: 1) y"- 3y"+3y'- y = ť°e' ; y(0) = 1, y '(0) = 2

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Q: 2 3. y' + ²y = -x²y²cos x

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Q: (c) y" - ry +y = ', y(1) 1, g/(1) = -1, r>0

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Q: (x 2 0, y 20 3x + 4y s 12 (x + 2y 2 2

A: In the given question we have to find the region for which x and y which are grater than or equal to…

Q: x, y) Edy is

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Q: 2 xy VI+x y)-ー1

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Q: 7. | y² dA, D= {(x, y) |–1< y< 1, -y -2 < x< y} D y - dA, D={(x, y) | 0 < x < 1, 0 < y< x} x + 1 8.

A: On solving these integration we will get

Q: y' + 2y = 1 + e−x, y(0) = −4

A: This is the first-order differential equation; it is in the form of Therefore, Then find…

Q: • V, = x - 2 • Y, = -x. %3D + X x y y -2 -2 -2 -1 -1 -1 0. 1 2 1, 2. 2) 1.

A: Here, we are given three functions. We need to find the corresponding tables and draw the graphs of…

Q: 73.xy-z(x- y)' (19)

A: 73 Given expression is xy−zx−y2. We have to find the value of the given expression x=3, y=-2 and…

Q: Ax, y) = 3y + x x>0 y>-2 8x + 12y 5

A: first we take equation place of inequility

Q: y""-2y" +5y +26y=0, %3D y(0) = 0, y' (0) =1, y" (0) = 1

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Q: P(x, y) = 68+8x-3y; subject to: x20 3x+2y < 44 x<3y y22

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Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

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Q: + 2y = 7x +4; y(0) = 3, y'(0) is y(x) =. %3D

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Q: 1- find y' for y =5x-3/x^2+2x. 2- find y' for y=(1+x-x^2)e^x.

A: 1- find y' for y =5x-3/x^2+2x. 2- find y' for y=(1+x-x^2)e^x.

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.