Problem 11. Y' + 2Y = f(t), where f(t) = t, 0 <<< t < 1 0, t≥ 1 and Y(0) = 0 Use notion of unit step-function write in a compact form ft). Then use Laplace transform of function and Laplace transform of derivative to solve given differential equation.

Q: Question 26 Find y' by implicit differentiation for 2y³+4x2 – y = x6 . - V 6x5 – 8x (A 6y2 – 1 6x+…

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Q: (c) Find the differential of the function: l =e"sin(s+ 21 )

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Q: y" - 2y' = -4 y(0) = 0, y'(0) = 4

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Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

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

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Q: The function y = x4 is a solution of the differential equa x²y" - 7xy' + 16 y = 0. Find a second…

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Q: Find y' by implicit dif ferentiation for 2y³+4x² –y = x6 . 6x5- 8x y '=- 6y2 – 1 A 6r5 + 8x B 6y2– 1…

A: Given, 2y3+4x2-y =x6 We have to find y' by using the implicit differentiation.

Q: Solve the IVP y"(1) +y'(t)- 2y(1)= 2e' sin(t), y(0) = 1, y'(0) = 1. %3D

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Q: Find total differential of function u = x.

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Q: Q1) Solve the differential euqation  dy/dx = xe^(-y) where y(1) = ln(1/2)

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Q: find all functions u(t) that solve the equation u'(t)+t*u(t)=-t * e^(-t^2), subject to u(0) = 1

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Q: 6y"" + 5y"+y' = 0 y (0) = -2, y'(0) = 2, y" (0) = 0

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Q: 7. Find y'if y=x³+ sin (x)

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Q: Solve the following differential equations. TT 1. sec'x dt = tan?t dx when x = t=" 2 4 |

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