x' + 3x f(t); x(0) = 1 where %3D f(t) is given by the graph below.

Q: Integrate (x)(e^-x)dx within the limits of (1, infinity)

A: Givne that  Integrate (x)(e^-x)dx   limits of (1, infinity)

Q: Calculate d2y dx2. y = e−(x − 3) − x

A:

Q: Find integrating factor of the equation (x4+y4)dx-xy3dy=0

A: The given equation can be rewritten as   xy3dydx=x4+y4    ∴y3dydx-y4x=x3     Let y4=t…

Q: 1) S dx 9-x2 dx 2) J2y-2 x2Vx2 -2 3) dx 2 V1-x2 |3D

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Q: arctan x Xe fel Xaresecx d

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find y': y = ez² + 3x² + e²e Oy = e + 3x ln x + e²ex Oy' = e + 3x²-1 Oy = e + 3x² In a Oy = e +…

A: Given y=e12x+3xe+e2e Given query is to find the derivative y'

Q: Q1) Find for : dx 1) y = log3(3x3 + x²)² × In(sec-1 vVx) 2 – (x² + y)² + (x – y²)² = x³ + y³

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Q: . The derivative of y = xe + e" is D. ex А. хе В. хе + е^ С. exе-1 + е‑

A: Given: y=xe+eπ

Q: 2. The rate at which the total average of COVID cases is dx increasing at x = 10 tents and 1 tent…

A: The solution are next step

Q: Calculate  d2y dx2. y = e−x + ex d2y dx2 =

A:

Q: Example 3: Estimate S, x² dx with n=4 by Midpoint Method. Solution:

A: Here first we will divide the integral range into 4 equal parts and then we will calculate the…

Q: 2x+2 dx. 5. x2-2x+1 dy 6. 5. if y = (1+ x²)etan-1x

A:

Q: Evaluate: e-y- [²" [m(x + y) - 7] dy dx In(x 0 x

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Q: -2x y" + (e by = 0 (e-* = z) -

A:

Q: a) The marginal profit for a product is modeled by dP -0.0002x + 14. 2 dx Apply the integration to…

A:

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: Use variation of parameters to find the general solution: x^2y''+xy'-y = ln (x)

A:

Q: d’y - 2 y = 5x' + In(x²). dx

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Q: 1. S(x* + x*)dx 2. S(x* + 3Vx)dx 3. Sx(1 – x²)dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3. LLa (x + 2y) dy dx

A:

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

A:

Q: 3. Find dy/dx y=3^(x^2-1) x ln(3x-5)

A:

Q: dy Q1) Find dx for : 1) y = log3(3x3 + x2)2 x In(sec- x)

A: I supposed to do only first question as our company guideline. Please repost other question as next…

Q: x - 3 7. S V25- (x-2)2 dx 8. S tan5 (2) dy

A:

Q: 10. x = Vt-2, d²y y =t2-3' dx2

A: The given question is taken from the derivative and we have to find the derivative of the parametric…

Q: Solve for dy/dx. y=((5x-3)/(4-3x))^-3

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Q: dy Y = y° dx 'x

A: As per guidelines,we will solve only first question.

Q: 4- S" e-x* dx 5- Vy e-y² dy

A:

Q: Solve y at x=1. dy/dx - 2(x+1)^3 = 4y/(x+1)

A: The given differential equation is dydx-2x+13=4yx+1

Q: The Integrating factor of the equation (x²y³ + xy) dy dx 1 is

A: We have to find the integration factor of the equation x2y3+xydydx=1. We know that integrating…

Q: find dy/dx: (x+y)3+ (x-y)3=x4+y4 ?

A: The given equation is x+y3+x-y3=x4+y4. Find the derivative dydx using implicit differentiation as…

Q: 1. (2x -х-у)dx- хdy - 0; y(1) -о

A: Given that: (2x2-x-y)dx-xdy=0; y(1)=0

Q: By differentiating x² – y² = 1 implicitly, show that d²y | dx² ||

A:

Q: 1,- X73X+2 dx (x+リ) Izafhinx dx Ax. Iォfュース alx dx X43X+2 X+1

A: Since, you have posted multiple, we will solve only first part. If you want solution of other…

Q: [4] s **-2x³-2x x²+1 [4] S² > [5] S dx dx ex-1

A:

Q: What integrating factor should be used to find the solution of the equation ydx + (xy + x- 3y) dy =…

A: Given that: ydx+(xy+x-3y)dy=0

Q: Solve for dy/dx and d2y/dx2 of : y=(x^2e^-x)- 4e^x

A: The function is y=x2e-x-4ex. Find the value of dydx using product rule as follows.…

Q: Find dy/dx for following: 1- Y= sec\x 2- Y= 2Vx X 3- Y= log2 8

A: We can make it easier for you.

Q: Use integrating factors to solve (x² + y² + x)dx + xydy = 0.

A:

Q: x(y-3). * - xly-3) dy = x(y-3)dx nly-31= C y-3 e [y-ce 3 2. Pesticide was given to a colony of 8000…

A: we have been given an equation y'=x(y-3) which can be written as  dydx=x(y-3) here, we will use…

Q: if y =(ln x +1)(2x3 -3x), then dy/dx will be _________

A: Use the formula of differentiation of product of two functions to solve this problem.

Q: 3x 6 1 -In xy dx e-In √x dx +dy +=dx = e-mxx y X

A:

Q: Vaz x² S. (2) dy dx

A:

Q: (x-G -0 +2) dx + 2(x+2y+2) dy:

A:

Q: find dy/dx for y = -(3x^2 + 5x)^5.

A: solution is given below.

Q: 1. ſ e3*dx dx 2. S- ex+1 dx 3. S. x/x² – 1

A:

Q: (b) Integrate x-³e-l/a², dx

A: Here we can find the answer as below.