By differentiating x² – y² = 1 implicitly, show that d²y | dx² ||

Q: (3y + 2x) dx –x² dy = 0, given that x = 1, when y = 2

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Q: Q2 /Find dy/dx, if: (1) x y+y =x2 (2) y = 3x* -5x' +10 у -

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Q: Find the solution of (x-2)dy = (3x² - 6x - y)dx given y(0) = 4.

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Q: a. By differentiating x2 - y2 = 1 implicitly, show that dy/dx = x/y. b. Then show that d2y/dx2 =…

A: The given equation is

Q: 1 Q2: Evaluate fo y² (x² + y²) dx dy

A: Given :∫01∫01-y2y2x2+y2dxdy

Q: Find d2y/dx2 implicitly in terms of x and y. xy − 1 = 2x + y2

A: xy − 1 = 2x + y2 We need to find  d2y/dx2 implicitly in terms of x and y

Q: for all of dx 1- y = xvInx 2- y = 3 x(x-2) x²+1

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Q: Evaluate " " So s L dz dx dy rvZ c3y (8-x²-y² Jx²+3y²

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Q: What is f P-(x)dx if the given DE is y(6y2 – x - 1)dx + 2xdy = 0?

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Q: Obtain the particular solution when x = 1 and y = 1 3 y°) dx 3 - x(x + y) dy = 0

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Q: (xy + x)dx = (x²y² +x² +y² + 1)dy

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Q: Find the General and Particular solution of = 4y ; y= 3,when x = 0 dx

A: Given: dydx=4y

Q: Find d²y if y =x² +3x-7 and x=2t+1. dt?

A: y=x2+3x-7 and x=2t+1

Q: dy= (x+1) G-2) dx メy

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Q: Find ax dy x-2–1 given y = 2x3

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Q: : x d²y dy dx² dx + +my = 0, given that

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Q: -2 (x² - y²)²] Evaluate: S₁ S² P₁² dx dy x+y

A: Let's evaluate given double integral.

Q: d²y 2) Obtain a particular solution for d*y dx+ + + y = x³ + 2x +1 dx2

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Q: Q4 Find dy for all of : dx 2- y = 3 x(x-2) x2 +1 1- y = xvInx

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Q: find the function y(x) satisfying dx/dy=5x ^(-6/7) and y(-1)=-2

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Q: Find d2y/dx2 implicitly in terms of x and y.

A: To findd2ydx2

Q: Q4 Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) %3D x²+1

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Q: (x + 2y – 1)dx + 3(x + 2y)dy = 0

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Q: Find dy x 3 In (x - y) = xy + y²

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Q: Find the General and Particular solution of = 3y ; y= 3,when x = dx

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Q: If y=f(8x²) and f'(8)= -3, find dy dx |x=1

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Q: (x³ + y² + z) dx dy dz. 2 Evaluate

A: To evaluate the integral

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

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

Q: d²y B Show whether y = Ax² + · x2 is a solution for x2- dy + x dx + 3y = 0 or not. dx2

A: If y=Ax2+Bx2 is a solution for x2d2ydx2+xdydx+3y=0...(1) then it satisfies equation (1).

Q: Find d2y/dx2 implicitly in terms of x and y. x2y − 3x = 8   d2y/dx2 =

A: Consider the given function, x2y-3x=8 use implicit differentiation method and differentiate with…

Q: x (xyx)dx = y(xy2)dy wheen x-2,

A: As per Bartley guidelines we are supposed to answer only one question per post.  This post contains…

Q: (c) Find the specific solution to d²y dx² when x = 0,= 0 and y = 1 +4 dy dx + 5y = 0

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Q: Determine the general solution of (x – 2y) dx + (2x + y) dy = 0.

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Q: B dy x/1-y2 dx 1+x2 II

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Q: d²y dy + 3x+y = 4sin (In(x)) dx²

A: Given Euler differential equation is: x2y''+3xy'+y=4sin(ln(x)) Let us take x=ez Replace:…

Q: + 2e* – 4V¤)dx , where f(0) = 7 -

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Q: If f(x)=3^x x^3, what is dy/dx?

A: Solution: Here  f(x)=3xx3

Q: Find the solution y = y(x) of dy y2 +y dx 0, x3/2 subject to y(1) = 1.

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Q: I am not sure how to do this. For the linear function y=f(x)=1x−3 Find df/dx, at x=5

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Q: Q11) The solution of (1 – y² )dx + (1+ x² )dy = 0 is: %3D

A: 1-y2dx+1+x2dy=0 On simplification, we get ⇒1-y2dx=-1+x2dy⇒dx1+x2=-dy1-y2

Q: If y = x3 – 2x2 + 3x – 1, then d2y/dx2 is equal to

A: topic - derivatives

Q: df Find and dx of dy 2 2 f(x,y) = /3x +4y?

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Q: Find the particular solution of (x+ y)dx +(x – y)dy = 0; when x = 1 y = 1.

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Q: If y = = e2a + e3x, then d y at x = 0 equals dx3 %3D

A: Given: y=e2x+e3x

Q: Find the solution of: dy 2y 3x when x = 1, y = -1 dx 2у + ||

A: A differential equation of first order is said to be homogeneous if it is of the form dydx=Fyx. It…

Q: Find the Particular Solution: y(x - 6y)dx - x(2x - 9y)dy = 0 ; when x=1, y=1

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Q: Find the general solution for d²y_2dy +3y = x² 2 dr2 dx

A: We have to solve given differential equation:

Q: Find the solution y = y(x) of y2 dy + y - dx = 0, x3/2 subject to y(1) = 1.

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Q: Evaluate S. (x – y)dx + xydx where C is the y = 2x2 – 1 from the point (-1,1) to the point (2,7).

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.