Use Laplace transforms to solve the following differential equation: y" – y' + y = t given y(0) = y'(0) = 1.

Q: y²y" = y³(y')² – yy'

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Q: Sove the differential equation given the condition y(0)=6   dy/dx = (x/y)

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Q: find the differentials of the first and second orders u=xyz

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Q: Find the differential of each function.

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Q: Is the following a homogenous differential equation? dy/dx = (x2y-y2x)/(x3-y3)

A: Let's find

Q: z = f( a, b, d, c), write the exact differential of the dependent variable

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Q: Sketch the direction or slope field of the differential equation. Be sure to show any "trends" and…

A: Given,y'=x-2y+1 x y y' 0 0 -2 0 1 -1 2 2 0 2 1 0 3 0 1 4 0 2

Q: 1 +x y

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Q: y" - y = 4 cost y (0) = 0 y'(0) = 1

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Q: (3) Using differentials, approximate the value of ₹28.3. Give your answer to 4 decimal places.

A: We are authorized to answer one question at a time, so we are answering the first question, please…

Q: form the differential equation corresponding to (y – b) = 4(x -a) %3D

A: Given: The equation is (y-b)2=4(x-a)   To determine: The differential equation from the equation…

Q: y (t) = cie' + czet – 3te + cos t –

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Q: Sketch the direction or slope field of the differential equation. Be sure to show any “trends" and…

A: Given differential equation is y'=x-2y+1                   (i) Direction field of the given eq. (i)…

Q: Find the function satisfying the differential equation 3/ – 4y = 6e"

A: Given the differential equation as y'-4y = 6e6t It is 1st order Linear Differential Equation Compare…

Q: Solve the differential equation e'y (x+2) (x²–1) * dx

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Q: Find the differential of the function. P = 99 - 293/2 dp = X

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.