Find the particular antiderivative F(x) of f(x)=4x−3 that satisfies F(1)=8.

Q: What is the integrating factor of y' = x - 2y? O 2x €2x Ox²

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Q: Find the most general antiderivative. X - dx ..... O A. - 3x2 - 3x3 +c 1 x* O B. 1 +C 2x - 4 4. 3x…

A: W we have to solve the integration

Q: The integrating factor of + 2.xy= 5x² is dx dy а. b. x2 e 2 C. 1 d. et

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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: use Separation of Variables to find the general solution. dx/dt= (t + 1)(x2 + 1)

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Q: Find an antiderivative F(x) with F ′(x) = f(x) and F(0) = 0. Is there only one possible solution?.…

A: Given, F'x =fx  fx = 2+4x+5x2   We have to find Fx

Q: Obtain the general solution of y√(1+x^2)dx+ x√(1+ y²)dy = 0 using variable separable method.

A: solution is given below..

Q: Obtain the general solution of: y(x°ey- y)dx + x(y + x°e*Y)dy = 0

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

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Q: 2. 2y (x²-y tx) dx-(x²-2y) dy = 0

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Q: 9. Find the most general antiderivative of the function a) f(x)=12+ sin x b) f(x)= 3x(x-5)

A: see below the answer

Q: dx dt -x + y + 2et ip dt — у — е-t

A: System of differential equation

Q: Differentiate √(xy) + 2x = √y explicitly with respect to x. Show your solution

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Q: ӘТ ӘР V

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Q: Obtain the General Solution of dx + xydy = y²dx + ydy.

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Q: y4) + 2y" + y = 0

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Q: II. Find the particular antiderivative of the function f(x) = e" (2" – 1) whose graph passes through…

A: Given

Q: If x =0.71 and y = 0.67, then value of C in the xsin-(x) V1-x² antiderivative of F(x) = is

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Q: Given a general antiderivative of x² + 3 +C with initial condition (2, 0), then the particular…

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Q: Find the general solution for y' = x – 4xy using an integrating factor.

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Q: Differentiate y = (2x + 1)°(x³ – x + 1)*. Solution: In this example we must use the Product Rule…

A: Given:- y =(2x+1)5(x3-x+1)4  To find:- Derivative of y

Q: Eliminate the arbitrary constants y Iny = C,e "+ C, X-

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Q: What is the integrating factor of the non-exact DE (4xy+3y² – x)dx+ x(x+2y)dy =0 2 A 2 © x²

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Q: 11) Find the antiderivative: f -3+6√x³ √√x dx

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Q: For an ideal gas, find explicit expression for the partial derivative:* ƏT RT P R. O Option 1 O…

A: The equation of an Ideal gas is PV=nRT. Here, P- Pressure V- Volume n- Amount of substance R- Ideal…

Q: find the general solution of dy/dx + (3/x)y=2/x^2 as a function of x

A: Given,           dydx+3xy=2x2

Q: 2(y-4x2) dx + x dy

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Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

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Q: Suppose f'(x) = 12√/1+4x where f(0) = 5. 1) Find the general antiderivative, f (x). 2) Use the…

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Q: dy _ 2y = x-'y¯1 y(1)= 3 dx

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Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: Minimize F(y, u) = f¿u²(t) dt under ý = -2y + u with y(0) = 1, y(1) = 0. Is your solution unique?

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Q: Find the particular antiderivative of the function f(x) = e"(2" – 1) whose graph passes through the…

A: Integration

Q: The integrating factor of the DE (x^2 + y^2 + 1) dx + x(x - 2y) dy = 0 is

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Q: Find the partial derivative for the function f(x,y)=√x+y3 f(xx,y)= f(x,y) = √8x + y² 33x √8x+y³ (y)=…

A: The given function is;  f(x,y)=sqrt(8x+y3).

Q: dx = x(x 1)(x + 1) dt has a solution that is

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Q: approximation of I = [" f(x)dx using composite Simpson's rule with n=4 is:

A: In this question, we evaluate the definite integral by using the composite Simpson's rule for n=4.

Q: What is the integrating factor of the non-exact DE (4xy+3y²-x) dx + x(x+2y)dy =0 ? (A) x² 1 B (U) D…

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Q: v(x² – y + x)dx + (x² – 2y) dy = 0 %3D

A: The given equation is 2yx2-y+xdx+x2-2ydy=0. Solve for the general solution using determination of…

Q: Given the function of two variables f(x, y)= ln(√x + 16). The partial derivative with respect to x…

A: Given, f(x,y)=ln(x6+y66)

Q: xsin-1(x) is If x =0.1 and y = 0.11, then value of C in the antiderivative of F(x) = V1- x?

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Q: Find the integrating factor of : 2y(x2 - y+ x )dx + (x² – 2y)dy = 0 ху O y 2х e2x

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Q: Find the most general antiderivative of f(x) = sin x cos x .

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Q: 2- y(x + y +1 ) dx – x(x + 3y + 2)dy = 0 Reducible to Exact Method

A: We have to find general solution of given differential equation which we reducible to exact method :…

Q: Reducible to dy 2х-у+4 homogenous method dx x+y-1

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Q: What is an antiderivative of x+2 ? x²+1 x + arctan x – 5 2x + 3 x + arccot x x + 2arctan x + 1

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