Find the solution of the following differential equations: a) x" + w?x = 8 (t-), x(0) = 0, x'(0) = 1 b) x" + 2x' + x = f(t), x(0) = 1,x'(0) = 0 Where f(C) = {6 (1 if 0st<1 to if tz1

Q: (1) The functions f, g and h are related by f(x) = g(x+1),. g'(x) = h(x-1), then f"(2x) equals: (a)…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: y" + 9y' + 7y = e-2t ,t > 0[

A: Using method of Laplace Transform.

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A: y' + p(x)y = f(x) can be written in the appropriate form dydx + p(x)y = f(x)  ⇒dy +p(x)y dx = f(x)…

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Q: y" – 2y' + y = ex x5 when y(0)=1; y'(0)=2

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Q: Given the differential equation y' = x2 + y? Take the Implicit Derivative of this function 2 times…

A: Given, the differential equation                                    y'=x2+y2 then take the implicit…

Q: (3-x-y)dy = (2x-4y+6)dr.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: y' + }xy = sin(x 4e¤2 y3 1

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Q: There are four questions about this problem in the test shown in random order. Out of 1000 customers…

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Q: Find the order and degree of the differential equation 1 5 (y"')³ = k[1 + (y")²]³

A: Given :y'''13=k1+y''252

Q: Solve these differential equations d. dy/(√x ln⁡2x )+dx/(y^2 ln⁡y )=0 e. xdx+ (ydx-xdy) cos⁡ (y/x)…

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Q: Find the general solution of the differential equation. (x'' 1) y' osx ca-y) こ

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Q: Consider the second order differential equation with initial conditions u" - 4.5u' - 5.5u = -4…

A: The given equation is u" - 4.5u' - 5.5u = - 4sin(3t)

Q: 5 9 บ” – ป + y = 1 + 3) - x+ 29

A: The differential equation is .We have to find the general solution of the given differential…

Q: Find the general solution to the differential equation x²y" – 3xy' + 13y = 4 + 3x 2. (where y' = )…

A: Given differential equation x2y''−3xy'+13y=4+3x......1. We have to find the general solution of the…

Q: 2. Use appropriate change of variable to reduce the order of differential equations and solve them…

A: To reduce the order of differential equation and solve.

Q: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

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Q: find a formula involving integrals for a particular solution of the differential equation…

A: The objective of the question is to find a formula involving integrals for a particular solution of…

Q: 7. The differential equation which has y = C1r + C2x as its general solution is: 4 (a) y" – -y'+ y =…

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Q: Perform the indicated operation. (303-j19) (j2-1)

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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.