Sketch the fol 2 -4y a-. b- y2 -4y 3(y - 5)2 C-

Q: Vy - y 3 b) dy 2 y²

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Q: - 5y = 2(x+ c)², dx

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Q: y' + z' - 2y = 1 z – y' = t %3D Yo = 20 = 1 %3D -

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Q: D'y- 4. (4D - 4D³ - 23D2 + 12D +36)y = 0 5. (D° + 3D² + 3D + 2)y = 0 Dy +y = 0

A: The given differential equation is: (4D4-4D3-23D2+12D+36)y=0 The auxiliary equation is:…

Q: - y² + 22 = 169 at (5,0,12). %3D (1) . i+3 3 3 -) i+ k, 6. 12 12 =) i+k, (d) k. i+

A: In this question, the normal to the curve is calculated using the finding gradient of the function.…

Q: y'' – y" + 4y'- 4y = 10e-t, y(0) = 5, y'(0) = -2, y"(0) = 0 %3D %3D

A: Given differential equation is y'''−y''+4y'−4y=10e−t, y0=5,y'0=−2 and y''0=0 Take Laplace transform…

Q: 7. x+y (2r +2y-x)' at (0, %) -4 at (-3y3. 1) 8.

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

Q: ux.ュメトXス1いスコ-Y Palx, utェッズ)-。 入2コメ; +メュ-」+5- メレ 2 d、しズuメッ]= xit Xzメ]-6 fnd in Ganeral rm.

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Q: 3. (Dª – 2D³ – 13D² + 38D – 24) = 0 4. (D² – D – 6)y = 0; when x = 0, y = 3, y' = -1 %3D

A: We have to solve the DE.

Q: Sketch Z= 2x^2 + 3y^3

A: Given, Z=2x2+3y3 To find: Sketch the plot for Z

Q: 2y" + 29y = 0, %3D y(0) = 7, y' (0) = 7. y(t) =

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Q: Find x and y in terms of a. X + y = 0 х+ ay %3D 6 (а + 1) (х, у) —

A: Given:    x + y =0        --------1   x + ay = 6     --------2 from 1: x = -y put the value of x in…

Q: (a) x²y "-xy '+ y = Inx %3D

A: According to our guideline, We can solve only first question of multiple question.So here we solve…

Q: · (D² + 3D + 2)y = xsin 2x

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Q: 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = -4

A: To find the solution of the given differential equation .

Q: d3y find 3 5) If y = 4x + z %3D dx3

A: Given that: y=4x3+3x2

Q: Find y dy √y+2 using the substitution u +5=√√y+2.

A: Follow the procedure given below.

Q: y(t) = y" - 3y' = 8e²t - 2e-t, y(0) = 1, y'(0) = -1

A: Given

Q: 9. (D² – 2D + 5)²y = 0 10. (D² – 2D – 3)y = 0 when x = 0, y = 0, y' = –4 %3D -

A: We will solve auxiliary equation then we will find the solution.

Q: Dyy 2y-x; %3D

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Q: - 6y(t) = 0; y(0) = 2, 1 %3D %3D

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Q: х-2 y = at [-1,1] x²+1

A: The given problem is to find interpolating polynomial for the given function and interval using…

Q: calculate d2y/dx2 when y=0.4x-0.3

A: use this formula:

Q: y" +2y'+ y = t O y = t-2 O y= 1/2 (t) O y = t O y = 2t -1

A:

Q: „T7/8 6) (1 + etan 2x) sec² 2x dx 16) B) - D A) e C) 2e

A: Given query is to find the value of the integral.

Q: * dy -a 2. 2xydx 2) yy +36 X =

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

Q: d'y if-8x-7y = 10. Find %3D dx2 Provide your answer below: -口 dy dx² FEEDBACK

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Q: dz (D² + 16)³(D² + 4D – 5)²(D² + 2D – 3)*z = 0, Dz = %3D %3D dr

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

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Q: Operator 1/f(D) 5. (D2 + 16)y = 4sin3xcosx 6. (D – 1)²y = 3cosh²x

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

Q: f(x) = (4e2x)3 3(4e2*)2(4e2x) 3D3(16e**)(4e2*) 192(e6x) %3D %3D %3D

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Q: d²y if 2x2 + 5y² = 9. Find %3D dx2 Provide your answer below: -口 dy dx2

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Q: (D³ + 7D² + 19D + 13)y = 0 when x = 0,y = 0,y' = 2,y" = -12 %3D %3D

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Q: dy un 3 sec2 5x, w dr

A:

Q: Evaluate d2y/dx2 at the point (0, -9). x = t3 - 3t y = 3t2 - 9

A: Given: x = t3 - 3t y = 3t2 - 9

Q: a.) = y° (4 – y²) - b.) y' = y In(y+ 2) %3D c.) = (ye" – 9y)/e" -

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Q: Show for Re(2) > 1 ez - 1dr = r'(z) 5(2). %3D 0,

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Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. y =c,e+ce+c,e²r+c,cosx + c zsinx y =…

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Q: 4. (D3 – 4D² + 4D)y = 0 5. (2D4 – 3D3 – 2D²)y = 0 - -

A: (4). The given differential equation is: D3-4D2+4Dy=0 So, the auxiliary equation is: m3-4m2+4m=0

Q: y" +2y' + y = t O y = t-2 O y = 1/2 (t) y = t O y = 2t -1

A: To find the particular solution to the given differential equation first write it into operator…

Q: y = 1+(t- y), 2<153, y(2) = 1, with h = 0.5 %3D %3D

A:

Q: Sketch Z= 2x^2+3y^2

A: To sketch: Z=2x2+3y2.

Q: Find y dy √x+2 using the substitution u +5=√√√y+2.

A: We will evaluate the given integral by using substitution method as shown below

Q: 4. (Dª + 2D³ – 6D² – 16D – 8)y = 0 - - - %3D

A: The given differential equation,     D4+2D3-6D2-16D-8y=0

Q: esents the center. 105° (4y +14) (7y +1)° (7x +1)°

A: We can see that this is a quadrilateral which is inscribed in a circle. Such a quadrilateral is…

Q: 3 1 (x + 2y)dydx -1 a) 5 b)7 O d)-:

A: Please check step 2 for solution.

Q: action: dx y = Jo x+3x-5 %3D

A: Integrate the following function:∫032x+3x2+3x-5dx

Q: dx Vx²-4x-7 7. dy y2-8y+5

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.