1- , S" cos(x)esin(x)-8y dydx

Q: Find y' if y= cos (X-1) X-1

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Q: 1 - cos 2x if y = prove 1 + cos x y' = 2tanx.sec²x

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Q: (sin°(3x) + sin²(3x)) cos(3x) dx

A: We have to find the indefinite integral.

Q: 5 Find y' if cos (Xty) =

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Q: y"" - y' = 2e-* - 3e2x when x = 0, y = 1, y'= -1 and y" = 2

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Q: JO (5) Find the derivatives (a) d # t ( * cos(2³) dz + 35e) 4

A: Since you have posted multiple questions i can do first question as per our company guidelines.…

Q: graph of (x) = x' - 2 is shown in the figure. Find 6 such that if0 2 ]x - 4] 2 8, then IAX) - A. ô =…

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Q: 6) Find X 11 df dx by using chain rule if f=u+= cos² u G(x)= U=πX 7) Say whether the function is…

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Q: e-y = y ¹ cos(2x) y(1) = yo

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Q: Find dy Y= #an" (=) + cos "(sx) + CoS

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Q: d csc 'x dx -1 Prove that xVx? – 1 2.

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Q: If t²y" – ty – y = 0 ,y(1) = 3 and y'(1) = -1, then y(4) = . . . %3D

A: Given differential equation, t2y''-12ty'-y=0,y1=3,y'1=-1 Find the value of y4.

Q: 1- x Vx2 + 9 dx. 1 2-5 dx 1+ sinx 3- sin'x cos'x dx

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Q: Which of these functions (or none of them): (1) z=e" (ycosx-xsiny) or (2) z=e' (y cosx-xsin x) 0²z…

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Q: y''''+8y'''+32y''+64y'+39y=e^(-2x)((4-15x)cos3x-(4+15x)sin3x) Find a particular equation for:

A: The given differential equation is: y''''+8y'''+32y''+64y'+39y=e-2x ((4-15x) cos3x-(4+15x) sin3x)…

Q: Find y' if y= is-2x(+)* +

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Q: If y = xsinx then prove that y''+y=2cosx

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Q: (tanx) y' = y, y(플) = 플 T

A: Given differential equation:- tanxy'=y

Q: 2) (3x²y+ 4e)dx + (x³ + 4xe + 2y)dy

A: We are authorized to solve only 1 question, please repost remaining questions Differential equation

Q: 5 cos? (- x), then f' ) %3D is

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Q: Identify which of the following functions require chain rule application to obtain their…

A: Chain rule is applicable for Composition of two functions only

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

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Q: f(x) = cos3(4x-1) Differentiate the equation

A: Given that: f(x)=cos3(4x-1)

Q: 8e cos 2x dx csc(x) sec(x)

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Q: Find the GS for y""+y"+y' + y = 1−x + e* - COS X

A: Given differential equation y'''+y''+y'+y=1-x+ex-cosx

Q: y= (12,4 + x)* + (1+)(Va² +x- c )cos²(4x), c)cos²(Ax), 3)4( 3 y = (12,4 +x)* + (1+x' Зx +x — с y = ?

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Q: Find the derivative of y = x°e*. O a. y' = 3e*x2(e*+x) O b. y 3x2(e* +1) O c. y = e*x2(x+ 3) O d. y'…

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Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: y" - y'-y = cos(5t)

A: Solution :-

Q: +3x2, (V)² = sin³(cos³(*3**» dy b. Find dx %3D

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Q: 3) [I - cos х х

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Q: Js sec¹ (t) tan(t)dt

A: The given integral is .We have to solve this integral.

Q: Solve the Bernoulli's equation given below: dy 2 dx -y cot2x = y' csc2x O A. [(y )^(- 2)] sin 2x = -…

A: Use Bernoulli theorem to solve

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.