1-solve the differential equation using laplac transform if f(0) = 11 & f'(0) = 28 d²y d²x - dy dx - 6y = 0

Q: Solve the linear differential equation using Fourier transform.

A: The objective of this question is to solve the given linear differential equation using the Fourier…

Q: Prove that the differential equation is not exact ey (e" + ") - s/ = 0 2+ + -

A: Exact diffretaial equation

Q: Show that the transformation 2 = ln x transforms the differential equation 2 x ²³y" + Axy' + By=0…

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

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Q: Transform the differential equation 4y′+2y=t^(5) y(0)=9 into an algebraic equation by taking…

A: The given differential equation .Using the Laplace transformation to find an algebraic equation and…

Q: sin(2t +) dt eu-3 %3D 64

A: Let, I =∫0∞sin2t+π2e2t-3dtApply integration by part ,Ist function = cos(2t) , since sin(π/2+x) =…

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

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Q: solve the follwing Euler's differential equation x2y''-7xy'+16y=0

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Q: Find the function satisfying the differential equation R' – 3R = 4et and R(0) = -1. %3D R =

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: Construct the differential equation of the family of curves xy=C(x-1)2 where C is an arbitrary…

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Q: Use Laplace transform to solve the differential equation y"-2y'-3y=0 with the initial conditions…

A: A linear homogeneous ordinary differential equation can be solved using the Laplace transform apart…

Q: Solve the differential equation  2y" + 60y = 2x2y" + 4xy'  . Then evaluate the Legendre polynomial…

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Q: (x²+y)dx + dy 0

A: This linear differential equation

Q: Determine the differential equation that corresponds to each slope field. No explana- tions…

A: 5. a) The slope field is,dydt=f(y)

Q: O Solve the differential equation by method of undermined coefficients d'y d'y 6dy =2e* dx' dx? dx

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

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Q: d) Solve the differential equation of y"" + 4y' = sec 2x

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Q: Solve of differential equations by the Laplace transform -2t x' - 5x -e ", x(0) = 3 %3| | |

A: The solution of the given differential equation using laplace transform is solved below.

Q: product rule to 3. Use the substitution uy to solve the differential equation xy' + 5y = 3ay

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Q: nd the solution of the differential equation = Z 3 + sin(z) with i dz

A: Given: dfdz=z-23+sin(z)f(0)=2

Q: Solve the differential equation 5y" - 5x2y" -10xy' + 100y = 0 . Then evaluate the Legendre…

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Q: Solve the differential equation x" + x' = sin(2), x(0) = 0, x'(0) = 1 by using Laplace transforms.

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