Solve the following initial-value problems: (x + y)²dx + (2xy + x² − 4) dy = 0. y(1) = 4

Q: ] Solve (3xª – y)dx + (x – 4x²y³)dy = 0.

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Q: Use computer software to obtain a direction field for the given differential equation. Sketch an…

A: Use computer software to obtain a direction field for the given differential equation. Sketch an…

Q: dy = 2x(1+y²) ex²

A:

Q: 1. Solve the following first-order equation: (2.ry +3y?)dr - (2ay+a)dy = 0. %3D

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Q: 1 (2x-3)4 4. S dx

A: Follow the procedure given below.

Q: 3.2 (2x - y²) dxdy

A:

Q: Q. x2y′′+2x2y′+(x − 3/4)y =0.

A: As per the question we are given the following 2nd order linear differential equation : x2y′′+ 2x2y′…

Q: 1. (x + √y² + 1) dx · (y – H.W. solve the following D.E. xy - - √12241) dy = 0

A: Step 1:

Q: 4. y(y² - 2x²) dx + x(2y² - x²)dy = 0 [Answer: x²y² (y² - x²) = = C

A:

Q: Solve for Z. X= (Y-Z) 3

A: Given: X=23Y-Z We have to solve for Z.

Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: Solve the following edo y²dx + (x² + xy + y²)dy = 0, y(0) = 1

A:

Q: x (х+1) dw solve for dx W 2х-1

A: The Quotient rule: fg'=f'·g-g'·fg2 The product rule: f·g'=f'·g+f·g' Given: w=xx+12x-1

Q: Solve the following D.Es: 1. (x+ 1) = x(y² + 1). dr

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: y ≥ 4/3x − 4

A: We first make a table for y =4/3x − 4 and draw the line using it. Picked few values for x, for those…

Q: dx 43. Evalua Jx +2)(x² +4x + 10) te

A: To simplify this integral, we use partial fraction decomposition. Thus,…

Q: 1. (x+6у?)dx - 4хydy-0

A: Given problem:- (x2 + 6y2 ) dx -  4xydy = 0  Solve the given differential equation

Q: (c) Solve for each of the following. dx (i) Vĩ + Jỹ = 4 (ii) y = 2x2+1

A: We have to find the first derivative of given function.

Q: 3. Solve the following: 2xdx (x²+1)2 a. b. y = f xe* dx, given y=0 when x=0 x-2x+1 dx с. d. sn (Inx)…

A: According to our guidelines we can answer only first three sub-parts and rest can be reposted.

Q: III. Solve each of the following: 3. (x - y - 2)dx + (3x + y − 10) dx = 0

A: Solution is given below:

Q: Solve for the values of Ay and dy if y= f(x) =x² + 2x? – 3x + 5 and x changes from 2 to 2.10.

A: Given: y=fx=x3+2x2-3x+5 And x1=2 &  x2=2.10  a). We know that; ∆y=yx2-yx1 So,…