(1)Find the general solution for (- x) dx – (-y) dy = 0

Q: Ex. Find the general solution to dy 1 -2.x dx X -

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Q: Find the general solution of 2 (y + 1) – (x + 1)/y + 1]dx + (x + 1)dy = 0.

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Q: solve. (exy + e²) dx + (zey + e*) dy + (ey −exy - e'z) dz

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Q: Solve the equation dy 2 dx with the initial condition y (1) = 1. 2/3

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Q: Find general solution of: 2x ( y - x^2) dx + dy = 0

A: Topic:- solution of differential equations

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

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Q: cos y dy – x sinx dx = 0

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Q: 2. (3x-y-4)dy -(x+y-4)dx=o

A: Given :

Q: ) Obtain the particular solution of (2x-3y+4)dx+3(x–1)dy =0; when x =-1, y = 2 O Find the general…

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Q: Find the general solution of dx -3 y=2cos3x . dx

A: The given differential equation is. d2ydx2+2dydx-3y =2cos3x This can be written as, D2+2D-3y=2cos3x…

Q: Z4 e: 2₁₁ (4x²yz - ) dz dy dx 1 4

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Q: dy is dy xy dx dx The general solution of y² + x² "

A: Solution is given below:

Q: 1 1 d y dy 2 3 X - х —- %D dx dx

A: Topic = Differential equation

Q: б бу-гу2 -14-292 y dx dy

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Q: Find the general solution for (y + 1) dx + (4x – y) dy = 0

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Q: dy Find the particular solution of the differential equation of x-y = 4x' sin(x) with the dx…

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Q: (v² +3 yx)dx +(3x² +cos y-e' )dy = 0.

A: It is problem of exact differential

Q: 3X e dx 3x + 3 X e a) S x sin (4x) dx x-y=-1

A: As per guideline we have to solve only three SUBPARTS from one question. Since both questions are…

Q: (x² + y²)dx – xy dy = 0

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

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Q: Solve the particular solution of 3y(x^2 - 1)dx +(x^3 + 8y - 3x)dy = 0; when x = 0, y = 1

A: The given differential equation is 3yx2-1dx+x3+8y-3xdy=0. The initial condition is x=0 when y=1. The…

Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

Q: The general solution of y2 + x2. dx e dy xy is = dx

A: Given: y2+x2dydx=xydydx ⇒dydx=y2xy-x2

Q: Solve the Euler equation d²y dy -x +y= dx dx (In x-1)

A: Solution

Q: Solve the particular solution of (xª + y³)dx – 2x° dy= 0 when x = 2, y = 3. -

A: We can rewrite the given equation as,  (xy+y3)dx = 2x3dy xydx+y3dx = 2x3dy

Q: 1. Solve the equation 3(y+1)dx-(x+y+3)dy =0.

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Q: Solve the bernoulli equation dx/dy+(2/x)y=-x^2y^2cos(x)

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Q: The general solution of (y-1)dx −2(x+y+1)dy=0 by CL2V is

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Q: (x + 2y – 1) dx - ( 2x + y - 5 ) dy = 0

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Q: dx - My- dy -5+e

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Q: Solve for dy/dx. y=((5x-3)/(4-3x))^-3

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Q: 2 1. Z =- 1+x2 ; d²z/dx?

A: z=21+x2

Q: 9. Find the General and Particular solution of = 4y ; y= 3,when x dx

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Q: I. Find the general solution of the following: 2 dy = -2x + 3x -2x = 3e dx (x²+5)dx- (2y - 1)dy = 0…

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

A: Take integration on both side and then put initial value

Q: 4- S" e-x* dx 5- Vy e-y² dy

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Q: Categorize the Differential Equation. (x – y)dx + (3x + y)dy = 0

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Q: dy dy = xy + 3x – 3x dx dx

A: The given differential equation is: dydx-x2dydx=xy+3x-3x3Therefore:dydx=xy+3x1-x21-x2

Q: y2 - cos(x²) + + 3x³ = 4x-3 dy 8. x – %3D dx

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Q: 4. if x^3+y^3=2 find the value of (d^2y)/(dx^2) at the point (1,1)

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Q: Find the general solution of the separable differential equation. xy dx+ sqrt(xy) dy = 0

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Q: Find the general solution of (y + 1) dx + (4x – y) dy = 0

A: Since we are given with multiple number of questions and our guideline is solve the first question…

Q: Find the differential equation y(x – 1)dx – (x² – 2x – 2y)dy = 0

A: Given differential equationyx-1dx-x2-2x-2ydy=0Compare the above equation with Mdx+Ndy=0Here we…

Q: 1. Solve: dy e" y- = e=Y+e=2z-y dx

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Q: 1. Find the general solution of 3 + = y*(2x*) dx

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: f- dx dt - 4x=2e²¹ + e*; where x(0)=0

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Q: 2 Z - 6 A xy dy dx dz 3.

A: ∫03∫09-z2∫0xxydydxdz

Q: 3x 6 1 -In xy dx e-In √x dx +dy +=dx = e-mxx y X

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Q: 2Y – x²y² -2. dy dx

A: The given differential equation is: dydx=2yx-x2y2

Q: [2x.ex dx=2x.e-fe.2dx =2x.e- er.2 =2e* (x-1) H.W. 2-1x3.ex de 3- f x2. cosx dx 들 27

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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.