(x + 2y - 1)? dx = dy A. x + Arctan { [V(2)] [(x + 2y -1)] } = c B. x = Arctan { [V(2)] [(x+2y-1)]} +c C. x + Arctan { [v(3)] [(x + 2y -1)] } = c D. x = Arctan { [V(3)] [(x+2y-1)] } + c

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A: Given: 3y2(x2-1)dx+(x3+8y-3x)dy=0initial condition is x=0,y=1

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A: Answer and explanation is given below

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A: Given that                          y=x+1x2x-3

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A: Using method of Linear Differential Equations with constant coefficients.

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A: By using partial differentiation.

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A: We will evaluate the following Integral.

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A: According to our guidelines we can answer only one question and rest can be reposted.

Q: solve the DE:   (2y^3-x^3)dx+3xy^2dy=0 ; y(1)=1 using 3 methods.

A: Let's find.

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A: Partially differentiate with respect to x and y by using product rule.

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A: By using linear differetial equation method

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A: That's computational, take a careful look.

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A: As per our company guidelines we are supposed to answer only the first question. Kindly re post the…

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Q: Transforming - Ⓒ S 1 = ²2²1dz 1+z² ℗ B / 1 + 2/2 d -dz 1-z² Ⓒ *2-2z² 1+z² (A) dx secx + C-²₁- -dz…

A:

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A: SOLUTION-

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A: See this solution in below

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Q: 2. (9y-2 +6y-4-y-5+1) dy 3. √ (12x²-x²+x²) dx

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Q: y" – 10y' + 34y = 3x2 + x – 1 || | (D² – 10D + 34)y = -cos3x

A: 1-D-1 = 1+D+D2+D3+.... Note : As per our Guidelines, we are supposed to answer first question.

Q: 1-x²-y² /1-x2-y2 1-х2 (x² + y²)dz dy dx -/1-x2

A:

Q: [ a(x+y) - xty]dy = (x+xy²- 2y +3)d« when x-1, yal 3. %3D (9xy - 2y²) dx - ( 6x²_ xy) dy =0 4.

A: I have authority to answer one question only, if you want another question to be solved then upload…

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A:

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

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A: