Prove that the equation below is a homogenous one and solve for its equation. 3(3x2 + y?) dx – 2xy dy = 0 -

Q: 3. (x² + 6y²)dx – 4xydy = 0 , y(2) = 1

A: Problem is in the form of homogeneous form...so put y=v.x and proceed as I have done solution step…

Q: 5. Find the general solution of the given DE: 2x + 2xy2 y + 2x?y dy dx

A: First We will separate X and y terms of the given differential equation and than integration gives…

Q: dy Solve for the value of C in the equation: (1-2x)dx when y(0) - 1 3y3 3

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Q: 47. Solve for the general solution of (5x+3y-4) dx+(x+y-2) dy=0. a. 5x2 + 4xy + y? = C b. 4x? + 5xy…

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Q: Obtain the general solution of the following equations. 3. (4xy + 3y²)dx + x(x + 2y)dy = 0

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Q: 2) Determine the constant A such that the equation (x² + 12ry) dx – (Ar² + 8y) dy = 0 is exact and…

A: The differential equation P(x,y)dx+ Q(x,y)dy =0 is an exact equation if and only if…

Q: 3. Show the equation (1+ e*y + xye*)dx + (xe* + 2)dy = 0 is exact and solve it.

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Q: B) Find the general solution of the equation by using (Undetermined Coefficients method) d'y dy de =…

A: Solution of the differential equation using undetermined method

Q: How can we solve this separable equation? N(y) * dy/dx = M(x)

A: The given differential equation is, Where, N(y) and M(x) are the functions of the variable y alone…

Q: Use Bernoulli's equation to solve for the general solution of the following. 1. dy/dx - y = 2xy^2…

A: then given equation is dydx-y=2xy2e-x it is the Bernoulli's first order differential equation of the…

Q: dr - (x- 2) ey dy = 0

A: Given Differential equation is linear. We will solve it by finding integrating factor

Q: noose a non-exact equation and solve. (xy - 2y?)dx - (x2 - 3xy)dy=D0 1. 2)

A: Q(1)  We have to solve given non exact differential equation:

Q: 4.a) Is the equation Exact? * (y2 – 2xy + 6x)dx + (-x² + 2xy – 2)dy = 0 O Yes, the equation is…

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Q: Solve the following using the method of solving Bernoulli Equations. dy 2. - 2y – x²y? – x²y² dx

A: According to Bernoulli's equation, we will have to assume some variable in such a way that another…

Q: Find an integrating factor and solve the given equation. (12x + 3) + (4²+¹2) = 0 12y dy dx

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Q: Try this: Solve the following DE. 1. (1+ 3xsin y)dx - x² cos y dy = 0

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Q: The general solution of V – 2x)dx+(2xy+ 1)dy=0 is?

A: (y2-2x)dx+(2xy+1)dy=0y2dx-2xdx+2xydy+dy=0y2dx+2xydy-2xdx+dy=0d(xy2)-2xdx+dy=0Now integrate both…

Q: Test the equation for exactness and solve the equation (2xy − 3x^2)dx + (x^2 + 2y)dy

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Q: Solve the following using the method of solving other substitution methods dy 2. dx sin(x – y)

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Q: Solve the following using the method of solving other substitution methods dy x+ y- 1 dx 3.

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Q: Use appropriate substitution to reduce the following equation to a variable separable and then Зх +…

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Q: Find the particular solution to DE:   ( y + square root of x^2 + ?^2 ) dx - xdy = 0 ; y ( √3 ) = 1

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Q: Solve the IVP. Show the steps of derivation, beginning with the general solution. Problem 1.3.16 y'…

A: Solve both of differential equation in the following way:-   In the first differential equation,…

Q: dy d. x = y + y³cosx dx е. dx - y = 2xy²e-*

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Q: (y? – 2xy + 6x)dx – (x² – 2xy + 2)dy = 0 - - -

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Q: non m Q4) Solve the D.E= %3D dx ya

A: Differential equation

Q: (1 + y²) dx + (x²y + y) dy = 0.

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Q: Test the exactness of the following equation then solve the equation: y In(y) dx + (x – Iny)dy = 0 -

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Q: z = xy dy x + y = 2x/1-x²y² 2. Using the substitution change the "dx to a separable equation. Hence…

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Q: dy Determine given: dx ax*y3 – bxy = 36 where a and b are constants.

A: Given query is to find the derivative of the expression.

Q: 2. Obtain the particular solution when x = 1 and y = 1 y(? - y? + 1) dx – x(x² - y? - 1) dy = xlx? -…

A: Here is the solution of the given differential equation.

Q: Solve the given IVP. x²° = y² + xy y(1) = 1 %3D dx Hint: Use substitution to change the equation to…

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Q: Test the DE for exactness then solve. 5. (3x2 + e2y)dx + (2x e2y – 4y)dy = 0

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Q: Show if the following statement is true or false. If it is true, write TRUE. If it is false, write…

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Q: Solve this completely to answer several questions. dy 4y Consider the equation- dx = X. What is the…

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Q: (x² + 3xy + y²) dx – x² dy = 0

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Q: #3 Test the exactness and solve the equation. (2xy 3x²)dx + (x² + y)dy = 0

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Q: 2. Obtain the general solution using Bernoulli's equation. Simplify your final answer. 3 (2y° + x/…

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Q: Solve the equation (1 + x cosy) dx - x²siny dy = 0 using substitution.

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Q: From the following equations select the one that is not exact and solve. (x2- у) dx — х dy%3D0 1.…

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Q: II. Solve the following first order DE. (x² + y²)dx + xy dy = 0 4.

A: Explanation of the solution is given below...

Q: the general solution of DE x2 dy/dx=4x2+7xy+2y2

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Q: QI: Solve the following DE: e*dx-ydy 0y(0) = 1

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Q: Do as indicated: 1. Solve the DE: (xy'+y)(1+2e* +e +e*)- xe = 0 *)-xe*: %3D

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Q: (2xy-ey)dx + (x2-xey)dy = 0 Find the general solution of this differantial equation.

A: (2xy-ey)dx + (x2-xey)dy = 0…

Q: Evaluate the dy/dx of the equation x2 + 3y? – 2x + 5y – 12 = 0. Evaluate the dy/dx of the equation…

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Q: Determine the constant A such that the equation (x2 + 3xy) dx + (Ax² + 4y) dy = 0 is exact and solve…

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Q: Solve as required : Given : Z = 3x?y³ – 4x*y? from the given, solve the followin d) e) Zxy f) Zoxy

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Q: Using the substitution x= X -3 and y= Y-3 show that the equation dy y+3 dx x+y+6 can be reduced to a…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.