Use the Laplace transform to solve the given initial-value problem. Be sure to allow time for uploading your solution. No emails please, es y" - 5y' = f(t), y(0) = 1, y'(0) = -1 8 4 L{f(t)} = S-4 S + 1

Q: If false state why.

A: Given,

Q: Q3. Solve in terms of Bessel's function, the ODE x²y" + xy' + ((lnx)² + ¹) y = 0 1²)y=0_z=lnx.

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Q: y = (x² – 1)lnx

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Q: 5 8 (OT-7) dt ||

A: SOLUTION-

Q: Find the GS of x²y" + 2xy' - 2y = 0

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Q: Compute and interpret f'(1) for each function above. f(r) = 6x2 + 3x 4 f'(1) = %3D

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Q: Find all local extrema for f(x)=x2e2x in the first cycle of the curve. Be sure to show a test for…

A: To find all local extrema for the following function. Note: Since, the student has mentoned to find…

Q: 4 Use implicit differentiation to solve for y' if r4y2 - x³y + 2xy³ = (Show your work)

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Q: Q(0)=135 Q'(t)=k(Q-70) Calculate Q at t=1 second and k=-8/second

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Q: find y as a function of x if: y'''-13y''+42y'=60e^x, y(0)=11, y'(0)=24, y''(0)=21

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Q: If f(x) = 5x¹(²), find ƒ'(6) to 3 decimal places.

A: The given function,   f(x)=5xlnx

Q: Find the GS of y" - y' - 12y = 0

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Q: Calculate the derivative.

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Q: Find dy/dx by implicit differentiation   √(x + y) =  1 + x2y 2

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Q: Find yy as a function of x if y′′′−7y′′+12y′=6e^x y(0)=30,  y′(0)=19,  y′′(0)=12

A: y′′′−7y′′+12y′=6ex        y(0)=30,  y′(0)=19,  y′′(0)=12 given differential equations is linear…

Q: maximum point of y x – 2

A: Condition for Extreme Value: A continuous function fx, y has extrema at a, b if fx=fy=0 at a, b…

Q: Compute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2

A: To find the second derivative of f at x = 1. The approximation formula for second derivative at a…

Q: If f(x) = x' – 8x + 2, find f (-4).

A: We have,  fx=x3-8x+2           ⋯⋯1

Q: Let z = x"y . If x increases by 2% and y increases by 3% then using partial differentiation theory…

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Q: Find f. 13 f"(x)=x³+ sinhx, f(0) = 4, ƒ(2)= 5

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Q: 2x 5. F(x) = "(5t – 1) dt

A: Here, it is given that F(x)=∫x2x5t-1dt

Q: Step 2: Step 3: Sten 4:

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Q: Find the equation of a curve if d²y 4 = dx² (2x - 1)² the curve passes through (5, 2 ln3), and the…

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