2x2 is an antiderivative of f(x) and G(x) = 3x° is an antiderivative of g(x). Find Suppose that F(x) = –- 3 (f(x) + g(x)) dx. Provide your answer below:

Q: 2x2 +4 Find the general antiderivative of f (x) =sin (x) + x²

A: Antiderivative is another name for integration of f. Therefore to find the anti derivative of f we…

Q: Find the solution using Variation of parameter. (D2 – 1)y= ex +1 'y=Gje"+ Cae"* + 글 xe"-e-1 ex – 1 4…

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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: In the given question , find d2y /dx2 implicitly in terms of x and y :-   xy - 1 = 2x + y2

A: In the given question , find d2y /dx2 implicitly in terms of x and y :- xy - 1 = 2x + y2

Q: the most general antiderivative function Find f(e) Sx-4+3x %3D t has

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Q: 4. xydx + (y √ x² + y²-x²) dy=0

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Q: In each exercise, obtain the particular of solution. a. (y + Vx2 + y²) dx – x dy = 0; when x = V3, y…

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Q: Find the particular solution for (2y3 – x3) dx + 3xy² dy = 0 when x = 1, y = 1 A. 5x²y3 = x5 + 4 B.…

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

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Q: A: Compute dy at (2, 1) where y = xcos2x dx B: Solve for x: a2 (y³ + vx-4 +y sin2x) < 4cos2r Тдхду…

A: Please see the answer below.

Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: Find the general solution using variation of parameters. y" – 4y + 4y = (x + 1)e²"

A: Given differential equation is, y"-4y'+4y=x+1e2x The auxiliary equation is, m2-4m+4=0m-22=0m=2,2…

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

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Q: 3. Is y(x) = C,sin2x + C2cos2x, where C1 and C2are arbitrary constants, a solution of y" + 4y = 0?

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Q: Find the Particular Solution: y(x - 6y)dx - x(2x - 9y)dy = 0 ; when x=1, y=1 O a. y (2y-3x) = 3x? O…

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Q: y3 r³ – 4x – 1 = 0 3 Find dy/dx and explain why dy/dx is always positive. Where on the interval [0,…

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Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: Obtain the general solution. 1. y' = xy?

A: We will find out the required general solution.

Q: Given the non exact DE y(8x-9y)dx+2x(x- 3v)dv=0. find f(x).

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Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

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Q: Use the method of reduction of order to find a second solution to t’y'" + 2ty' – 2y = 0, t > 0 Given…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Use the technique of variation of parameters to find a particular solution to the DE y" – 2y + y =…

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Q: Sin²y dy V1 -x, given that y(-3) = 0. dx 2) Snow that the general solution for (x2 +x-6)dy = 4y dx…

A: Given that  The following differential equations

Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: Find the general solution to t²y + (t + 1) y =t', for t > 0.

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Q: Is y = cīt + cf is the solution to y" – 12y = 0? Prove it

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Q: i) ais f(x,y) = x2 + 3xy + y -1 Laalic * Te Te

A: Given that  Af(x,y)=x^2+3xy+y-1  To find the partial differentiation of f(x,y)

Q: For x=e2 y=In 2t. find y' when x=e. O 4e e 4e O e -|

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

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Q: xy' – y = 2x lnx

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Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: g Solve Rour of the following D.E A)(xュ)dx + 2xy dy dy B) ャリ=ex c) (xx v y'es )dx -(y- )dy zo D) (X…

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Q: Solve the following using Integrating Factor by Formulas. a.) 2y(x2 - y + x)dx + (x2 - 2y)dy…

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Q: €x2 + 5х + C) dx %3D Зх + 5

A: Given: ∫32x2+5x+Cdx=3x+5

Q: What is the solution of (xy? – x) dx + (a²y + y) dy = 0 when x = 0 and y = 3 %3D O (22 - 1) (y² – 1)…

A: Exact differential equations.

Q: Find The Pollowrng in tograls:- Excersises 4 ( 2x + 6y x*) dy de (2 (ay + 29) dë dy + +) dy da x+4

A: As per our Guidelines we can solve maximum 3 question as per request , otherwise we solve one…

Q: B. In each exercise, obtain the particular of solution. (y+ Vx² + y²) dx – x dy = 0; when x = /3, y…

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Q: Find the most general antiderivative of f(x)=6e^x+5 sec^2(x), where -pi/2

A: Please see the answer below

Q: Find the general solution of the di f ferential equation *+ x .2 d²y + (x² – )y = 0.

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Q: Find the particular antiderivative that satisfies the following conditions: dy 4x-2 + 2x-1 - 7; dx…

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Q: The antiderivative of [Vx-25 dx is V x2 - 25 - sec-x+ C. A True B False

A: Given: I=∫x2-25xdx     As we know from the trigonometric identities; 1). sec2x=tan2x+1 2).…

Q: Find the particular solution for (2y³ – x³) dx + 3xy² dy = 0 when x = 1, y = 1 A. 5x²y³ = x³ + 4 B.…

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Q: The antiderivative of [Vx²-25 dx is x2 – 25 – sec-lx+ C. A True B) False

A: ∫x2-25xdx

Q: -13x b) y = S dx Integrate. x2-5

A: Explanation is given below..

Q: Show that xy – 2 = cxy is a solution of (x² + y2 – x)dx – ydy = 0.

A: Given  x2+y2-xdx-ydy=0 dydx=x2+y2-xy

Q: Determine the value of C if f(x,y) = C is the solution of (x+ 2y-3)dx+(x+2y+1)dy3D0 for x=94 and y=…

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