y" = 2x – 3, y(0) = 1, y(1) = 1,0 < x < 1 %3D -

Q: 2y(x² – y + x}&x + (x² –2y)dy = 0 2. Determination of integrating factors:

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Q: Discuss the Error in Differential Approximation?

A: Given: Discuss the Error in Differential Approximation?

Q: dx/dt+dy/dt+x=e-t dx/dt+dy/dt-x-y=e2t x(t) general solution function

A: Given equations are                                              dxdt+dydt+x=e-t           ...…

Q: Reducible to Homogenous method dy X-y-3 x-y-1 dx

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Q: Determine whether the equilibrium at x = 0 is stable, unstable, or semi-stable. dx 4x² - x³ dt 3 The…

A: We need to find the equilibrium at x=0 is stable, unstable, or semi stable. given,…

Q: Find both first partial derivatives. h(x, y) = e(x¹0 + 10 hx(x, y) = h₂(x, y) =

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Q: S2x²e** ax=uv- Jvau -Svau. Sfoxe". Using Integration By Parts, Find uv- Jv du- 3 x² e dx O 2 x3 x3…

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Q: 3 - y cos xy - 4x ) dx + (- 2x+3y x cos xy + 2y) dy = 0 - | 2x+3y 2.

A: Compare the given equation with Mdx+Ndy=0 to obtain M and N. Calculate the partial derivatives of M…

Q: integral of (y^2-14y+5) / y(y-1)(y-5) dy

A: ∫y2-14y+5yy-1y-5dySubstitute u = y-1=∫y2-14y+5yy-1y-5dyApply the Sum Rule:…

Q: 6. sin'x dx 7. cos*x dx 4x+ 2 dx x +x + 5 8. .2 (1+x*)dx 2x-1 dx 2-8x + 15 10. 2x+x +1 1. dx (x-1)…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 2х -1 dx Integrate dx by using substitution method. e*-x+1

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 3. Integration by parts: 3x d x (V3 2x+4

A: To find out the integration.

Q: Sxsecxtanx dk=uv- fvau -Svau- O 2x sec x - S2secx a 1 Using Integration By Parts, x sec x tan dx =…

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Q: 1. When is the exact method applicable? 2. When is separation of variables applicable? 3. Why is…

A: We have to answer the following questions. 1. When is the exact method applicable? 2. When is the…

Q: y = x - 2 sin(x), 0 sxs 27 aximum value inimum value

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Q: Classify the partial differential equation ´ôx² ôyôx ôy²

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Q: A ball is thrown upward from the top of a 200-foot tall building with a velocity of 40 feet per…

A: It is given that the ball is thrown upward from the height of 200 feet with a velocity of 40 feet…

Q: ar systems of differential eq + 2y = sint x - y' = cost x(0) = 0

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Q: x++1)dx 4 x²(x+1)²

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Q: 1. In a large tank there are 1000 gallons (gal) of water with a concentration of 1 pound (lb) per…

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Q: 8. y dx + 2(y -x) dy = 0

A: Linear differential equation in x.

Q: Find four second partial derivatives. z = e" sin(y)

A: Consider the function z=exsiny Here, the objective is to find the four second partial derivatives…

Q: Integration using Partial Fraction! dx X(x²

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Q: the integrating factor of the FOLDE y'-2xy=x is e^-x^2, show your solution

A: Recall: Linear differential equation of first order :    dydx+P(x)y =Q(x)…

Q: 3. Determination of integrating factors: 2y(x+ y+2)dx +(y² - x² -4x-1)dy = 0

A: The given differential equation is  2y(x+y+2)dx+(y2-x2-4x-1) dy=0. Repost the next question.

Q: 3x+4 3). S; (x2 +4)(3-x) dx (Integration by Partial Fraction)

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Q: 13. dx √ex-1

A: Given: I=∫dxex-1   ...1   As we know that; The Chain Rule: fgx'=f'gx·g'x And ∫1x2+1dx=tan-1x+C

Q: Find the integrating factor: x^2 dy+(2x^3 y-e^x )dx=0

A: First order linear differential equation of the form dydx+P(x)y=Q(x) Integrating Factor:…

Q: The linearization of ex at x = 0 Derive the linear approximation ex = 1 + x at x = 0.

A: Given, ex ,x=0 We know that, The formula for the linearization is, Lx=fa+x-af'a

Q: find a sets of solution. Integrating Factors found by inspection   x(x²−y² - x)dx− y(x²−y²)dy= 0…

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Q: Solve for the integrating factor y (x + y) dx + (x + 2y – 1) dy = 0 Option 1 Option 2 et Option 3…

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Q: The expression Tyi is an integrating factor for x²y³dx +x(1+ y²)dy = 0. 2xy³

A: x2y3dx+x1+y2dy=0                      (1) If 12xy3 is an integrating factor then multiplying it with…

Q: Q1: Find the Integration using Gamma Function Method: x*e-3xdx 0.

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Q: 3. What is a constant of integration? Why does an answer to an integration problem involve a…

A: Integration

Q: Solve the partial differential differential by separation of variables 3 + 7 0. %3D

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Q: d²x dx dx -(1) = 2 4- + 4x = 0 x(1) = 0, - dt2 dt

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Q: What is the integrating factor y(4x+y)day - 2(x^2-y)dx = 0

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Q: 2) (2x + sin x) dx + x cos y dy = 0 3) - 2y + a = 0 dx dy 3y 4) r2 (Exact). (Separation variables).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: (3z²+5z+3)dz (z- 2)(z+3) Integrate:

A: The given integral is ∫(3x2+5x+3)(x-2)(x+3)2dx

Q: Example 12 : Form the partial differential equation by eliminating the arbitrary function from z= xy…

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Q: Find both first partial derivative h(x, y) = e-(xª + y^) hx(x, y) = hy(x, y)

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Q: 4. A tank initially holds 80 gal of a brine solution containing 1/8 Ib of salt per gallon. At t = 0,…

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Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: Find the first partial derivative wx, wy, and wz of (x + yw )2 –  ez  – 2 = 0  Make the solution…

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Q: A. Integration By Parts 1. ſx5Vx3 + 1 dx 2. S/* x sin 2x dx 3. S- x³ex? -dx (x2+1)2

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Q: (a) Give two reasons why it is important to study analytical techniques for solving partial…

A: We shall solve first question only as per the company guidelines. For others kindly 1 post again by…

Q: Obtain a family of solution 1. [x-y arctan(y/x)]dx + x arctan (y/x)dy = 0

A: Solution is given below:

Q: B. Integration by Parts 1. xcosx dx

A: We know that integration by part formula is given as  ∫uv dx = u∫vdx - ∫dudx∫vdxdx To evaluate: ∫x…

Q: 1. Integration by parts: 2 3 .5x X°e dx

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Q: d2x/dt2 + 4 dx/dt + 3x = 2 x(0) = x’(0) = 0

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