dy The solution of the differential equation using Laplace transform 10y = est is dt „given that y(0) = 0

Q: Find at æ = 3 if y=-5x² - 2 and da dt dy dt = 4.

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Q: Let F(x) = dt. Then %3D 25 (t + t10)15 F'(x) = %3D

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Q: If t = x + ex, find d2x/dt2 given dx/dt = 1 / 1+ex.

A: dcdt=0 , where , 'c' is any constant. dexdt=ex .dxdt

Q: xx+24=5x² fpyonbouy of anyos

A: We have xx+24≤5x2 Consider:…

Q: dx Q1/ By Laplace transforms, solve the equation 3 dt - 4x = sin2t given that at t=0, x= 3

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Q: secx 1 Given g(x) : z dt , find g'(x). t2

A: gx = ∫7sexcx1t2dt           = ∫7sexcx t-2 dt        = t-2+1-2+7secx      =t-17secx-1 = secx-1-7-1-1…

Q: Find dx dt da dt at x = 5 if y=-x² - 1 and dy dt 1.

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Q: Let F(x) = sin 3t dt, please find F'(0)

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Q: dy at x = 1 if y = 4x² + 1 and dt dx Find – 1. dt dy dt || ||

A: Solve the following derivative

Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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Q: Find dx dt dx dt || at x = 5 if y = 4x² - 4 and dy dt = 3.

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Q: Let g(æ) = / e-(a - 21)" dt. Find gʻ(æ).

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Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: rsin( z)+1+c 1 Let c> 0, and define H(x) := dt. Compute H'(x). Be sure to 1H4 fully justify your…

A: We have given H(x):=∫-x2sin(x)+1+c11+t4dtWe apply Leibnitz's rule of…

Q: 3 Let r(t) = · (1 ²³₁,e², Vt-2). t-1 √ F(t)dt = { Evaluate the definite integral.

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Q: t2-6t+9 dy 3. y = 2-5t+6' dt (t+1)(t²–1) dw 4. w = t2+2t+1 dt

A: follow next step

Q: F(x) = J e2f sin² (3t)dt. Then F'(x) =

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Q: A tank initially contains 60 litres of pure water. Brine containing 2 gm of salt per litre is…

A: Using the given data.

Q: Suppose f(x) - 6'Vi+ť' dt. 1) Evaluate / (2).

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Q: W = x =t' +7, y=cos(2t), z=4t COS

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Q: dx dy dy Find and dt' dt dx X = 7te', y = 3t + sin(t)

A: Here, dxdt=ddt7tet      =7tddtet+etddtt(used product rule)      =7tet+et(1)      =7et(t+1) Now,…

Q: Suppose f(x) = [ 6t² /1+t° dt .

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Q: Solve by using Laplace Transform and explain the steps in brief d?x dx +2 +x= 3te dt? dt Given x(0)…

A: The given differential equation is: d2xdt2+2dxdt+x=3te-t  …1 Given: x0=4; x'0=2

Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: Let f(x) = 1 + x³ + dt. Determine the value of (f-1)'(0).

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Q: E. Find , and in terms of dx dt' dt 1. x = t°- 1 2. x = 4t + 3 y = 3t – 2 y = 4 - t

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Q: dx/dt = X +y dy/dt = 2x + 2y

A: To solve dxdt=x+ydydt=2x+2y