For y=In 2t, find the value of k so that ¿ky'=1 at x=e

Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

Q: y"+4y' + 3y = sin e*

A: Solving the differential equation by variation of parameters method

Q: Solve the following DE using variation of parameters (D – 1) y = e" + 1 -

A: Let's find.

Q: You tart muesting at t=0 y co) =0

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Q: Q5-Find for x? + cos(xy) = y dx

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Q: y to solve the following linear differe ] dy

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Q: Q1: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy? *

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Q: Q6A)If y = sin-¹ find Zxy. on

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Q: 1. Lif f(x,y,2)=2exp(-5xyz)cos(15z) Find ôxôz

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Q: e) tan 5y – y sin r+3ry? = 9.

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Q: Solve the following DE by using appropriate substitution. Evaluate y(x) explicitly. an dy Jy – 5x +…

A: Consider the provided differential equation, dydx=y-5x+4+5 Solve the provided Differential equation.…

Q: For x> 0, 음 S"규E dt = Itt? %3D

A: For x>0, we need to find ddx∫1x11+t2dt. Leibniz's rule for differentiation under the integral…

Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

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Q: 2 dy Is y = sin t, a solution to = 1 – y? Justify-

A: We will prove the given statement.

Q: Use appropriate substitution to solve the following (iv) zy" + (y/) 0. %3D

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Q: If y = 1+ sin t ,x = cost at t =; Find by using Chain Rule, then choose the correct answer: dt

A: We have to use properties of differentiation.

Q: Use the correet fransformation to Find the solution of the Problem below. 一00<Xく00 0< Y<1…

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Q: Find dy and evaluate when x = T and dx 0.5 for the function y -10 cos (5x)

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Q: dy Consider the IVP dx (2y – 3x)?, y(0) = 0.

A: Consider u as 2y-3x. Differentiate both sides of the equation u=2y-3x to obtain the expression of…

Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: Find a positive value of k for which y=cos(kt) satisfies y''+25y=0.

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Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

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Q: Find the devivatives of the following equation b Y= ln (x,4)-x fori CH/2)

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Q: Solve for the General Solution ds 5s = dt te 5t sin t %3D

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Q: If y = 1+sin t ,x = cost at t = dy Find- dt by using Chain Rule, then choose the correct answer: a)…

A: Given curve is  y=1+sint  ,x=cost

Q: If y = 1+ sin t ,x = cost at t Find by using Chain Rule, then choose the correct answer: dt

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Q: Find dy. y=cos(7 *square root of X)

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Q: Given f(x,y,z) = cos(4xy) + sin(2z). Find fy(1,2,0). Leave your answer correct to two decimal…

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Q: If xy + ey = e, find the value of y′′ at the point where x = 0.

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Q: Q6A)If y = sin-¹ prove Zyy + 2 = 0

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Q: If xy + ey = e, find the value of yn at the point where x = 0.

A: xy + ey = eWhen x = 0,  ey = e = e1Hence, y = 1

Q: Find the linear approximation at x = 0 to each of f(x) (x + 1)?, g(x) = 1+ sin(2x) and h(x)= e2*.…

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Q: differentiate h(y) =tan(10y)/e^(4y) +1?

A: To Determine: Differentiate the given function:…

Q: Given: f(x,y) = x³y – y cosh x" Solve for D132

A: Given:                   fx,y=x3y-coshxy To find: The value of the partial derivative D132.

Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: For the DE y" + 9y = sin 3x : Use Variation of Parameters to find Yp

A: Given differential equation is, y''+9y=sin3x. In operator form can be written as, D2+9y=sin3x…

Q: хуз dx + e** ,3 dy = 0.

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Q: Solve the following DE 3 X dy %3D

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Q: given dy=x+coS X find yuhere y( -1.

A: Using variable separable.

Q: The velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for all t.…

A: given the velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for…

Q: Solve for the DE equation associated by the given function: у %3D Ае2* + Ве* + С. а.

A: the given solution of differential equation isy=Ae2x+Bex+C

Q: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

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Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: Find L ft ={fe',01 el-s -1 b. 1-s e -1 et -1 а. 1-s C. 1+s e- -1 d. 1-s

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Q: π ,t<. 3 b) Let y(t)= 1? + sint , find L(y(t)) 3

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Q: For Cos(2) dx find Ty, My and S,

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

Q: If we have to check the DE (5-8y+4xy)dx = (x+2)²dy for Exact then My

A: M dx + N dy =0