Problem 1: Given the differential equation ( x²y² + x + y²+ 1) dx + x 2 dy = 0 with the condition y (1) = 1: a. Identify whether the differential equation is variable-separable, exact, or first-order linear. Show proof. b. Solve the particular solution of the given differential equation in implicit form, £(x, y) = C in accordance with its type shown in part a.

Q: 1. Solve the given differential equation (2xy*e" + 2xy" + y)dx+ (x*y*e" – x*y² - 3x)dy= 0

A: The solution is given as

Q: b) Solve the following second order differential equation, clearly showing all calculation steps dy…

A: To solve the given second order differential equation :-

Q: Solve the differential equation by separation of variables: yl= 6xy², y(0) = 1/ 3 Oy y = Y y Y 1…

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Q: a. (2ry*e + 2xy + y) dx + (r²y*e -x²y² – 3x) dy = 0; when x = -1, y = 1

A: As per our guidelines we are supposed to answer 1st question only. Please repost rest questions...…

Q: 1. (D²³+2D² - 5D (D³ + 2D² - 5D - 6)y=0; y = 0, Dy = 0, D²y = 1, when x = 0.

A:

Q: (y - x + 3)dx + (x + y+ 3)dy = 0; x = 1; y = 4

A: This is the question from differential equations.

Q: 3. Solve the differential equation of u(x), then substitute y back to obtain the solution of the…

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Q: Solve the following first order differential equations: 1.1 (x²y + xy-y)dx + (x²y-2x²)dy-0 by…

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Q: E.X; Let T = {E₁ = (-∞,a): a = R}U{R,Ø} be a topology on R and let A = [2,3), B=(3,4), C = (1,5], D…

A: It is given that,  T = Ea=-∞, a : a∈ℝ∪ℝ, ∅ is a topology on ℝ. We have to find the closure of the…

Q: Solve the following differential equations, say what type of equation it is: Separable, homogeneous,…

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Q: III. Solve the differential equation (4x - 3y + 13) dx + (4y − 3x −15)dy = 0 ; y(1) = 2

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Q: Find w, where w3 = 1 + i. i? = -1.

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Q: Q: Solve the following differential equation: In(y? + 1)dx 2y(х-1) dy = 0 у2+1

A: Explanation of the answer is as follows

Q: Find the general solution of the following differential equations: 1. (x5 - y²)dx + 2xydy = 0

A: Solution to the differential equation

Q: D

A:

Q: PART B: Find the general solution and particular solution of the following differential equations 6.…

A: Use separable variable method to solve

Q: Q: Solve the following differential equation: In(y² + 1)dx + 2y(x-1) dy = 0 y2+1

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Q: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

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Q: Solve the following differential equation by separating variables and solving for the EXPLICIT…

A: Given query is to find the solution of the differential equation.

Q: 3. Find the differential equation having the solution as of the following: a. y = ce-* + c2e¬2x + x…

A: The number of arbitrary constants in a given relation is the order of the differential equation of…

Q: b. ešy² dx + (e*y – 2y) dy = 0 |

A: Since you have posted a multiple question according to guildlines I will solve first question (i.e…