Solve the initial value problem. 5x2 - x – 4 (x + 1)(y + 1)’ 2 dy dx X y(1) = 1

Q: dy 2x + 1 y(-2) = -1. dx 2y

A: To solve the IVP: dydx=2x+12y, where y-2=-1. Solution: Separating the variables of the given…

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

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Q: Write each equation in the form M(x)dx + N(x)dy = 0 test for exactness and solve those equations…

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Q: Solve the given equation.. dy - 3y = x³, v(1) = 10 X dx a. y(x)= x²Inx+5x³ b. v(x)= x?Inx + 10x³ c.…

A: Please refer to the image below

Q: Determine the value/s of D if the graph of the equation x² + 4y² + Dx - 4y + 2 = 0 a single point;

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Q: ay (2х-10у), +y = 0 dx Solve

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Q: 3. Consider the equation (3x2 + 3y? + 6) dx + (kxy + 8y³ + 1) dy = 0. (a) Determine the value of the…

A: The solution is given as

Q: solve D.E. by using Linear (y? + 1)dx + (2xy+ 1)dy= 0

A: See the attachment

Q: 2. (x+53y)e dydx %3D -1J0

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Q: B Solve the following D.E y(6y² – x-1)dx+ 2.xdy = 0, y(6) =1.

A: Given: y(6y2-x-1)dx+2xdy=0, y(6)=1 The given differential equation is a bernoullie differential…

Q: Example 12: Solve: (y - 2xy)dx= (x² – 2xy)dy %3D

A: Given that :  A defferential equation is given.  Now solve it

Q: d²x 3. + 2x - x = 0, %3D dr (8x(0) = 1, x'(0) = 1; x(0) = , x'(0) = –1 %3D %3D %3D

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Q: Solve the diff eq (xy² + x- 2y +3)dx + (x³y - 2x – 2y)dy = 0

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Q: Solve th D.E using Exact (6x² – y +3)dx+(3y – x – 2)dy

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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: (xy² + x³y) dy + y³ –x*)dx = 0 y(1) = 0.5

A: Given differential equation, xy2+x3y12dy+y3-x4dx=0,y1=0.5 Find the general solution in the…

Q: у (4х + у) da 2 (x² – y) dy - - 2x2 + x + 2 ln y = C ans.

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Q: dy (d) 3y(x2 – 1) + (x³ + 8y – 3x) dx 0 =

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Q: Write each equation in the form M(x)dx + N(x) dx = 0 test for exactness and solve those equations…

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

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

Q: Determine for which values of m the function (x)=x" is a solution to the given equation. (a) 3,2d…

A: We have to find the value of m.

Q: Solve (x2 + 1) + 2xy = dy 2 dx x²+1

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Q: 3. Show that the equation (x²y)dx + () dy = 0 is exact and then solve it.

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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: Write each equation in the form M(x)dx + N(x)dy = 0 test for exactness and solve those equations…

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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: Solve the D.EXY+Y=1/1/2

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Q: dy yet sh te +2xy = e=x? dr Solve

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