2x-3 3. Let f(x) = 3x+4' ,find Y as Ax -0 Ay

Q: y(x²-1)dx + (x³+8y-3x)dy =0  when x=0, y=1

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

Q: 3 9 dx dt -1 -3 with x(0) : 4 Give your solution in real form. X1 = X2 = 2. II

A: The objective is to solve the differential equation:

Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

A: In partial derivative when take the derivative with respect to one variable consider other variables…

Q: Solve Separable (x – 4)y*dx – x³ (y² – 3)dy = 0 -

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Q: e2x-1 If y = prove that = 1- y² dx

A: Given :y=e2x-1e2x+1

Q: Find an antiderivative F (æ) with F' (x) = f (x) = 5 + 24:³ + 15z4 and F (1) = 0.

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Q: [(x²-y²)²] x+y -2 LEK 1J0 du dt

A: We have to find value of given double Integral.

Q: If x2 – xy + y? = 3 find y" (second derivative) 18 12 12 18 A. В. С. D. (x- 2y)* (x- 2y) (x - 2y) (x…

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Q: 4 the second order For the function y = 4 e" - - d'y is derivative dx? 4e + 8x-3 O 4e" + 4x-2 -3 O…

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Q: 3 2x+3 Integrate the following function: y = dx x²+3x-5

A: An integral expressed as the difference between the values of the integral at specified upper and…

Q: of of For the function f(x,y)% 9x2- 3y°-4, find and dx dy of II

A: While calculating the partial differentiation of a function with respect to X we consider the other…

Q: 4 + 8x is x2 The antiderivative of the function f(x) = %3D

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Q: kx 4+x² If k 1, evaluate k (a) 2 kx (b) 2 J₁ arctan (2x) + C arctan (2x) + C dx. (c) // ln(x² + 4) +…

A: Given: ∫kx4+x2dx We have to evaluate the given integral.

Q: 2. Find the General Solutioh oG (əx -3y-2) dx-Cx-2y) dy =0

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Q: -2 (x² - y²)²] Evaluate: S₁ S² P₁² dx dy x+y

A: Let's evaluate given double integral.

Q: f(x)= (ex+2 +1/e-x -14ex+1) / (xex-ex/x+1 +lnee^x) differentiate?

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Q: Q4 Find dy for all of : dx 2- y = 3 x(x-2) x2 +1 1- y = xvInx

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Q: 2. Find by implicit differentiation. dy dx 4 (a) x +xy +y = 5 2 2 3 =D5 3 2. (b) x- xy + y 3. =D1

A: Recall: An equation of the form f(x ,y)=0 , in which y cannot be expressed directly in terms of…

Q: V16-x² .4 Evaluate: [4 16-x² J/x²+y² dz dy dx

A: We will evaluate the following Integral.

Q: Q4 Find for all of : dx 1- y = xvInx 2- y = 3 x(x-2) %3D x²+1

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Q: (2) y(x) = 1+1 So (1 – 3xt)y(t) dt

A: Given that the equation is yx=1+λ∫011-3xtytdt Let take Kx,t=1-3xt Then yx=1+λ∫01ytdt-3xλ∫01tytdt. So…

Q: (-4x-12) dx For J x+10)³ (x-4)³ F(x) – 1. What is F(3)? -

A: Given: ∫-4x-12x+103x-43dx=Fx-1   ...(1)

Q: Find general solution of ODE   (x+y-1)dx-(x+y)dy=0 dy/dx = (x+2y-3)/(2x+y-3)

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Q: (2xcosy + 3x2)dx + (x3 − x2siny − y)dy = 0, if f(0) = 2.

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Q: [2x*yžcosx² – 2x*yå + x/5]dx + [x/5stnx² - x° /9]dy = 0 3 2x²yz + x [x/ysinx? – x³ /y]dy = 0 -

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Q: -4x+2 Integrate f6 dx with respect to x using the substitution method. (-2x2+2a-2) COMPLETE THIS IN…

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Q: a) Find if y = (1+2/x)°.x²® using chain rule. dx dy 1-x b) Find if y = using chain rule. dx 1+x

A: (a) To find: dydx if y=1+2x3·x23 using chain rule: Formula used: Chain rule of derivative:…

Q: x³dx =², then = f(x) is Using integration by parts to solve and letting u = V4-x2

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Q: QI Find dy for 2y2/3+xy3/20 x 0

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Q: Find the general solution: k^2 dx+(x-y+k)^2 dy3D0

A: Given that: k2dx+(x-y+k)2dy=0     NOTE: As per our answering guidelines, we can only answer 1…

Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvlnx 2- у %3 V x2+1

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Q: Find d^2y/dx^2 for; x-t^2 y=Dt^5-2t^3+1 *

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Q: 3. Find the General and Particular solution of = 3y ; y= 3,when x = 0 dx

A: Take integration on both side and then put initial value

Q: 3 d²y If the functions are x = e-t and y = t+t + 1. Determine its dx2

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Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: 4 + 9x is x2 The antiderivative of the function f(x) %3D

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Q: 4e-2t 6] d - x(0)= 1; y(0)=1 dt 1 8t x(1)=?

A: From the given matrix equations, we get:Given:A=-1210b(t)= 4e-2t-6 8t x0=1; y0=1To find: x1=?

Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

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Q: 11) Find a function y-f (x) that satisfies both conditions: d - 6x -4x+5,f(-1) =3 dx %3D dy 2 3 ==+…

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Q: 1-y Q2: Evaluate fo y²(x² + y²)dx dy -1

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Q: Find the Particular Solution: y(x - 6y)dx - x(2x - 9y)dy = 0 ; when x=1, y=1

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Q: 2. x3 – y3 = c³, find y" %3D d²x 3. x* = at?, find dt2

A: we need to find d2ydx2 from equation x3-y3=c3

Q: 1. f (x, y, z) = x° ỹ + 4z°y² – xyz + x² – Vz -

A: Given that: f(x, y, z)=x3y+4z3y2-xyz+x2-z53               NOTE: As per our answering guidelines, we…

Q: 7. Find for x2 + y² = y dx 2x а. 1-2у 2x b. 2у-1 с. 1-y d. y-1 e. None of the above

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Q: find explicit solution: x^2 dy/dx =y-xy       y(-1)=-4

A: Given differential equation is                                       here we can easily separate the…

Q: Find f(3,4) for f (x, y) = ln(x + Vx² + y²).

A: We have to find out the derivative

Q: .x(3xy-4y3 + 6)dx + (x³ - 6x²y2 - 1)dy = 0, when x = 2, y = 0

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Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative