x(t) = 121? – 12t, y(t) = -41 + 612 + 9t %3D %3D where t goes from 0 to 1. Answer:

Q: Higher Order L.D.E (D2-2D+10)2y=0

A:

Q: Is y = e-x + 2xe-* a solution to y" + 2y' + y = 0.

A:

Q: Find the particular solution of (y + Vx² + y²)dx – xdy; when x = v3, y = 1

A:

Q: d'y 5dy -3y = 0 dx 2- 2. Determine the general solution of

A: given: the differential equation is: 2d2ydx2+5dydx-3y=0

Q: 3x² (- x) dx – (-y) dy = 0 2х (1) Find the general solution for

A: The given differential equation is: 2xy3-xdx-3x2y4-ydy=0 Comparing this with: M dx + N dy = 0, we…

Q: Q2) Solve the D.E x²dy + (3xy – 1)dx = 0 %3D -

A: Given differential equation is x2dy + (3xy-1)dx = 0

Q: d²y - y = у 3 10sin?x %3| dx2

A:

Q: Solve the non-homo. D.E. 1.y" + y = 3e2x

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Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

Q: Get the solution: x^2 dy/dx - y^2 = 2xy

A: Get the solution: x^2 dy/dx - y^2 = 2xy

Q: dy-Hy-5 te %3D xp

A:

Q: d'y 4x dx2 dy +6- + у %3D0 dx

A:

Q: 4.2(х — у)dx + (3х — у — 1)dy 3 0

A: Let's find.

Q: Is y=V10 – x a solution of dx A) Yes B) No

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Q: Q2) Solve the D.E dy – (2x/1- y²)dx = %3D

A:

Q: Q2) Solve the D.E dy - (2x/1-y2)dx 0 %3D

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Q: Find dy for the given values of x and Ax, y%3D5X²-6x, x= -2 and Ax =0.1 dy =D (Round to the nearest…

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Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: Obtain the general solution. 1. y' = xy?

A: We will find out the required general solution.

Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

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Q: Solve the D.E x dy+ (2y-x-11dメ-0 (24-X-1)dxメ= 0 %3D

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Q: b, y" -zy'-3y= e*

A:

Q: Q2/ solve; dy A: dx y **= e* + y3 x+1

A: Consider the given differential equation as below: dydx-y(x+1)=exy3 Here the objective is to find…

Q: Y = 4x²-5 Vsx dy=?

A: We want to find derivative of y, The given expression for y is,               y=4x5-55x

Q: V16-y? /32–x²–y² V 22 dz dx dy

A:

Q: What is the solution for y(t)?

A:

Q: Find the solution. d3x d?x d³x dx + 2 =0 dr3 dr? dt

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Q: nd the general solution to: 2yy -e^ = 0, |

A: The question is taken from the calculus in which we have to find  the general solution of  given…

Q: e + xy + 4x = 1 ise y"(0) =?

A: ey+xy+4x=1 Differentiating with respect to x, we get…

Q: Find the solution 7. (x + 4y³)dy - ydx = 0

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

A:

Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: y"+ y't 5y-

A:

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: dy = 6 3y – x- dx

A:

Q: V9-r² S xydzdydx •3 (d) S So

A: We have to find value of given triple integration

Q: Find the solution. ,dy --y²=2xy dx A y B y = -(- -1 D 2x x-2

A:

Q: Solve the follawing D ·E. 2. y²dx + (3xy +y²-1) dy =0

A: Please refer the attached image for complete solution.

Q: Find the solution. dy x-+ 5y =2r2y4 dx

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Q: dy Find the general solution of xy + y² dr x2

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

Q: Q2- Reverse the order of the integration ff dy dx + f2f²dy dx equal:

A:

Q: Solve the 2nd order D.E. below using method of undetermined coefficients : y''+ 7 y' = 42 x^2 + 5x…

A: To find the solution, first, solve the homogenous ODE, y''+7y'=0 and obtain yh=C1+C2e-7x.…

Q: Find the value of k so that the value of (2y - 1) dy is 10.

A:

Q: Solve the non-homo . D.E. 1.y" + у %3D Зе2х

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Q: d³y Find dx3 where y = e*(8x + 1)

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Q: Given d'y dx² = 6x-0.5x², y(0) = 0, y(12)=0, Use step size h = 4, z1 = 20, and z2 = 25. Enter 4…

A:

Q: Use variation of parameters d²y +pdty+94=Fx) plem) to find a particular solution to y" – 2y - 15y =…

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Q: - (D² +2D+5)y=e* sin 2x

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Q: Solve the (1+) d x = (b an y -x) dy

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Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y (0) = 0.4, y' (0) = –0.4, y" (0) = -0.4

A: The Symbolic form of the equation is D3+D2-2Dy  =4e-2xcos x Auxiliary  equation is D3+D2-2D=0…

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: