y=x2x(x>0,x≠1)

Q: dy y² tion + dx x² है || Y 8

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Q: Find for y = x. -

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Q: 5) (x- 4)² + y² = 9 Center Radius

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Q: Find the general solution of y' = y secx

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Q: y" + 2y' +y = e-*

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

Q: Find y': y=- Vx* + 4

A:

Q: Find of y3 = x* + 3x d?y dx2

A: giveny3=x4+3xdiffrentiate with respect to x3y2y'=4x3+3y'=4x3+33y2

Q: T (3 sec² x + 4 csc² x) dx 3

A: The given integral,        ∫π3π43sec2x+4csc2xdx

Q: Simplify

A: Given: To simplify the expression       (2x2 y-5) (6x-3 y)…

Q: 은 J4-√x dx

A: This question can be solved using integration by substitution.

Q: dy ニ 3 x +y-2

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Q: dy :- 15x²y and y = 4 when x = -4 dx

A: To solve the initial value problem  dydx = -15 x2ydyy = -15x2 dx

Q: 18. V1+x dx 1-X

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Q: write the domain in interval notation.

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Q: f(x) = x2 cosh 3x -

A: Simply, I have used laplace transform formula.

Q: calculate d2y/dx2 when y=3/x

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Q: dx J-2 (5-4x-x²)/2

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Q: Differentiate y=2x/e^x

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Q: x3 dx J4- x4

A: ∫x3dx4-9x4Multiply & divide by -36 =-136∫-36x3dx4-9x4since, ∫f'(x)f(x)dx= 2f(x)

Q: Find d^2y / dx^2 when y = 8+x / 4-x

A: Simply take two times derivative of the given equation using the derivative of the form  u/v

Q: 3 csc2 V1-4cot² x x dx

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

A: To findd2ydx2

Q: Differentiate the function. y = (3x- 1)* (4 - x5) 3 dy dx II

A: To differentiate the given function:

Q: 8. Find when x = t3 -t and y = 4 –- t². dx'

A: Here, the given functions are: x=t3-t & y=4-t2⇒x'(t)=ddt(t3-t)=ddt(t3)-ddt(t)=3t2-1…

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: Differentiate the function. -2 y= [(3x2 +4x +5) (x – 4) < dy dx II

A: We can use the chain rule of derivative in order to solve the given problem.

Q: Integrate the function. 2+36 x dx 1) 9x2

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: (x4 - 4x²y²-y4) dx + 4x³ydy = 0; when x = 1, y = 2

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Q: (6x-y > -3 13. ly>x-2 14

A: First draw the two straight line 6x-y=-3, y=x-2.

Q: y = sec* ( Vsin(2t)) sec³ 3.

A: The objective is to find the derivative.

Q: Solve y(x)=1–2x–4x² +[3+6(x-1)-4(x-1)ʻ]y(t)dt it.

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Q: use Separation of Variables to find the general solution. y' = x sec y

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Q: Differentiate.  y =t / (t- 1) 2

A: To differentiate the function y=tt-12. Quotient rule of differentiation states that:…

Q: dydx x² +y²

A:

Q: Solve for y. y' = 7x + xy​; y = - 4 when x = 0

A: Given,  y'=7x+xy,  y=-4 when x=0

Q: y, = x2 + 2x + 2 Y2 = 2x + 18 dx 25- 20 15 y 10- 5- 6.

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Q: 4. y = vx + 2 x,for-

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Q: Solve for y when x=o degrees: y=2sinx

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Q: Solve: y(x) dy dx = = (8x² - 7x + 6) (y-7), where y(0) = 11.

A: We will solve the given differetial equation by variable separation method.

Q: sec x =dx Vtan x 3 8. 4

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Q: Find of y' (y-x)° = y² – x² dx

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: calculate d2y/dx2 when y=-2/x2

A: Given: y=-2x2

Q: dy y2+1

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Q: Solve for y in terms of x and z. z = xy

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: SV2*- 16 dx 2.x

A: Consider the integral: ∫e2x−16dxApply u…

Q: Help.

A: Take u = 1/x5.

Q: x3-1 dx J2+2x+5

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0

Q: "+y = sec³ x

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.