The equation (x - 3y)dy = (2y + 4)dx is exact.

Q: Determine the equation of one of the curves for dy/dx = 4x which passes through the point (2, 3).…

A: We need to find a curve for dydx=4x which passes through 2,3.

Q: 4X-) dx dy y2 ret -1

A: Given: ∫12∫-10ex2y-4x-1y2dxdy

Q: For the equation, 2y(x^2 - y + x)dx + (x^2 - 2y)dy = 0, what is dM/dy - dN/dx?

A: 2y(x2-y+x)dx+(x2-2y) dy =0M.dx+N dy =0M = 2y(x2-y+x)N = x2-2yNow.            dmdy =…

Q: Solve the equation dy, 3y + dx +2 = 3x, y(1) = 1.

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Q: Obtain the general solution to the equation. dy y +7x +1 %3D dx

A: Here we have to find general solution of given differential equation

Q: Find the general solution of the first-order equation dy/dx=(y^(2) − 2xy)/x^2

A:

Q: what is the general equation to the equation dy dx² dx

A: Here we have to find the general solution of the given differential equation,…

Q: [a - y)dy dx 28.

A:

Q: - у = 3x-2 4x-5

A:

Q: Use Bernoulli's Equation dy/dx=y-xy3e-2x

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Q: dy/dx=y2/3

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Q: If xy + y2 = 1, find the value of d2y/dx2 at the point (0, -1).

A:

Q: Solve dy d'y -8 +12y = 0 dx? dx .2

A: The objective is to solve the above differential equation.

Q: If x^3+y^3=2, find the value of d^2y/dx^2 at the point (1,1). the value of d^2y/dx^2 at the point…

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Q: -3 dx dy 0, y2

A:

Q: if y = 3x2-2x+5 , determine dy/dx using the definition.

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Q: Find the first and second derivatives. 6x5 y = - 7x+4 ex dy %3D dx dx II

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Q: Find the first and second derivatives. Y=4x^2-12x-5x^-4 dy/dx= d^2y/dx^2

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Q: Solve the equation dy a - x- = a dx dy + dx

A: The given differential equation is a - xdydx = ay2+dydx.First, we will simplify this.a - xdydx =…

Q: 15. In (x² + y² + 1) dx dy

A:

Q: Find dy/dx for the equation: y= (e2x+1)/(1-2x)2

A: The given equation is,

Q: Find the equation of the solution to dy/dx=x4y through the point (x,y)=(1,5).

A:

Q: The solution to (2x – 4y – 3)dy = (x- 2y)dx is:

A:

Q: y^2 dy/dx = 4 is:

A:

Q: Find the dy/dx: Given y = 3x +2x-1

A: solution:-y=f(x)=3x2+2x-1f(x+h)=3(x+h)2+2(x+h)-1             =3x2+2xh+h2+2(x+h)-1…

Q: x² - 3 y : х +2 dy dx

A: Given: The function is  y=x2-3x+2   To determine: dydx of the function y=x2-3x+2

Q: y = (ax-1) (6x.+5]%3 find dy dx 10

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Q: -4x-2 FInd given y =-2 dx Sx+3

A: By using partial differentiation.

Q: If x3 + y3 = 2, find the value of at the point (1,1). dx?

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Q: Obtain the general solution to the equation. (dy/dx)-y-e^3x=0

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Q: y = ( 2x³ - 8x )* Find dy/dx when x = -%

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Q: dy y 5. Solve dx 5(x-2)y2 %3D (х- 2)

A: We first convert the given differential equation into the linear differential equation, then solve…

Q: Solve: x- dx dy - (x + 1)(1 + y*).

A: First separate the variables than integrate and solve the  differential equation .

Q: y3 (3- e*)* dy dx

A:

Q: If yx^2 + y^2 = x, then the dy/dx is

A: Using derivatives formula.

Q: dy -y- dx 2x, given that when y=0, x=+2

A: We need to solve the given differential equation with its initial conditions. As the equation is of…

Q: ху+3x- у -3 dy %3D dx xy-2x + 4y- 8

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Q: y = (3x² + x-2)-1; 49 -1 , dy dx

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Q: Solve the DE: 2 dy 3 dx 3x² + y² xy

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Q: If y-2xy 21, then dy dx at the point (2,-3) is

A: We have to find dydx at the point 2, -3 for the equation or expression: y2-2xy=21 We know the…

Q: If 3x² + 2xy + y² = 2, then the value of dy/dx at x = 1 is

A: Given that        3x2+2xy+y2= 2 We have to find the value of dy/dx at x=1.

Q: -2y Six*y dx dy 3.

A: Given a double integral ∫12∫02yx3y dx dy we need to calculate This can be done as:

Q: Evaluate the integrals

A: Consider the given integral, ∫02∫-4-y24-y2∫02x+ydz dx dy integrate with the given order of the…

Q: what is the general equation to the equation dy dx 2 2 dx²

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Q: Match the options below: (2ху-Зу) dx+(x^2-х)dy-0

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Q: Find dy/dx and dx/dy from 6x-x'y +4x 0

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Q: Find dy/dx of  1. y=x3 (2x2 -1)

A: Given, y = x3(2x2 -1) Multiplying the x3  with (2x2 - 1)  So, y = 2x5 - x3

Q: Solve the equation. dy dx dx -- dy %3D

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Q: Find y subject to the conditions dy/dx = 2x – 3 and y(0) = 3.

A:

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.