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 y = 5.25x² +4.75 and dy Find when x = 4. dt dx dt 0.3.

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Q: dt = (c) (9+t2)3/2

A: Given:

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

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Q: et dt 3/2 +8 e' +

A: Given integral is, ∫ete2t+8et+732dt. It is integrated by applying u-substitution method, Substitute…

Q: e"dt=

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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: 1. How does your score in a test varies to its equivalent in percent? b. indirectly a. directly c.…

A: Hello, thanks for your question but according to our policy I am answering the first three subparts.…

Q: tan x If h(x) Vt + vt dt, then find ht(x). 0,

A: We apply here Leibniz rule

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

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Q: Compute the differential dy  for  y=(6x+sinx)^3

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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: olve the differential equation using Laplace transform. dy +4+4y=e-2t dt y (0) = 1 y'(0) = 2 d²y dt²

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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: 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: 4x Let F (x) = S dt. Find F" (x). %3D 2+3

A: Given: Fx=∫04xdtt2+3 we know that by fundamental theorem of calculus if gx=∫pxqxfxdx then…

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: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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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: Find dx dt dx dt at x = −5 if y = −4x² – 5 and dy dt = -4.

A: y=-4x2-5given  dydt=-4d dx(xn)=nxn-1d dx(constant)=0

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: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: Determine whether the sets S, and S, span the same subspace of R°. s, = {(2, 1, -2), (0, 2, 2), (4,…

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