Find the particular solution by means of Laplace and inverse laplace transforms of the following differential equations: 1. x”(t) + 2x’(t) + x(t) = 3te^-t ; x(0) = 4, x’(0) = 2 2. y”(x) + 2y’(x) + y(x) = x; y(0) = -3, y(1) = -1 3. y’ + y = e^(2t); y(0) = 0 4. x”(t) + x(t) = 6sin 2t; x(0) = 3, x’(0) = 1 5. y”(t) – y(t) = 4 cost; y(0) = 0; y’(0) = 1

Q: y''+y'=0 where y(0)=0, y'(0)=1 laplace transform of derivatives

A: Given that:-  y" + y' = 0 and y(0)= 0, y'(0) =1 We find laplace transform of this differential…

Q: Match the differential equation with its direction field. y' = 9(x + y) - 1 15 0.1+ -4.31 -0.2 -Q.1…

A: Matching the differential equation with its direction field  y'=9(x+y)-1 x 0 0 0 0 0.1 0.2 0…

Q: y²y" = y³(y')² – yy'

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Q: Is f(x) If so, √2x+3 find differential at x = 1? f'(1)

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

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Q: what value of n can be used to transform the Bernoulli equation y'+p(x)y=q(x)y^n into an equation of…

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Q: y" - y' - 2y = 5 sin x y(0) = 1, y'(0) = −1

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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: d. y= x² + y x + cos y

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Q: FInd the differential equation of the family of circle with center at the origin

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Q: Determine the solution of the differential equation shown using Laplace and Inverse Laplace…

A: Given y'''−y=4e−x+3e2x.....1 When, x=0, y=0, y'=−1 and y''=2 Take Laplace transformation of equation…

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

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Q: Find the solution r(t) of the differential equation with the given initial condition: r'(t) = (sin…

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Q: Find the general solution of the following differential equation: a) t * dy/dt = (1-y^(2))^(1/2).…

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Q: 4x3 y = x", y(0) = -3 and choose the correct answer from the followir x4 +2 Solve the initial value…

A: Note-  Acc. to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Cx²e*dx

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Q: Find a fundamental set of Frobenius solutions of the differential 4x² + x(7+2x+4x²) y'-(1-4x-7x²)y=0

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Q: find differential equation of the following equation 1) y' = y-x y+x

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Sketch the direction field for the differential equation. Then use it to sketch a solution curve…

A: The given differential equation is: y'=5y+25xy. We have to sketch the direction field and then use…

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.