1. Solve the following ODE using Laplace transform: 19 y" + 10y' + 24y = 144t², y(0) = 122, y'(0) = −5.

Q: use laplace transform to solve y'-y=2cos(t), y(0) = 4

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Q: Q5/Solve the following ODE using Laplace transform y" - 2y' - 3y = e-2x, y(0) = 2, y'(0) = -1

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Q: Use the Laplace transform to solve the following initial-value problem for a first-order equation.…

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Q: Consider the following ODE y' = y+t/y+1 Which kind of ODE is ?

A: Given ODE is y'=y+ty+1. Simplify y'=y+ty+1. ⇒dydt=y+ty+1⇒y+1dydt=y+t⇒y+1dydt−y=t..........1 Since,…

Q: Solve the following ODE using Laplace Transform: 1. 6y" + 5y" + y' = 0 y(0) = -2, y'(0) = 2, y'"(0)…

A: The given differential equation is                                            6y'''+5y''+y'=0 With…

Q: Q5/Solve the following ODE using Laplace transform y" - 2y' - 3y = e-2x, y(0) = 2, y'(0) = -1

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Q: Solve the following DE using Laplace Transform 3. y" - y' -2y = 5 sinx y(0) = 1, v'(0) = -1

A: The given differential equation .We have to solve the differential equation using the Laplace…

Q: Classify the following ODE y(4) -3y (3)-y' =0

A: We have to classify the ode

Q: Use Laplace transforms to solve the IVP y''-y=0, y(0)=2, y'(0)=3. Show the complete solution.

A: Given initial value problem is, y''-y=0, y(0)=2, y'(0)=3

Q: 2. у" + 2y'- Зу%3D бе -3t У (0) %3D 0, у'(0) %3 0

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Q: Q5/Solve the following ODE using Laplace transform y" - 2y' - 3y = e-2x, y(0) = 2, y'(0) = -1

A: We will use Laplace transformation table to find Y(s) and then use inverse Laplace transformation…

Q: Given that -9/s cos(9t) L{- Vnt Vi cos(9t). find the Laplace transform of L{V cos(9t)}

A: We find the required Laplace transform

Q: 3) Determine the inverse Laplace Transform. where f = L{F}. 4 F(s) = In s- 3, %3D

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Q: Use Laplace transform technique to solve , y"-y'-6y= 0, Given y(0) = 1 and y'(0) = -1

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Q: Use Laplace transform to solve the DE. d²y_3dy = 9 dx² dx where x=0, x=0 and dy=0 dx

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Q: t も c6 10. XCt)> { -8 + -8 t ct-6)? » t >6

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Q: 4. (20 points) Use the Laplace Transform to solve the IVP y' +2y 2e", y(0) = 3

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Q: 3. State and explain the Convolution Theorem for Laplace transform

A: We have to state and proof  the convolution theorem of laplace transform.

Q: Read each of the two statements carefully. Choose A(if both statements are true), B(if the 1st…

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Q: find the Laplace transform of VE cos(3Vf). E{VE cos(3V)} =0.

A: We are given that,  Lcos3tπt=e2.25ss..................................................(1) We are…

Q: Solve the following ODE 3t. y" – 6y' + 9y = t²et; y(0) = 0, y'(0) = %3D

A: Given The given ODE is y"-6y'+9y=t2e3t. y0=0,    y'0=1 Apply formula…

Q: y = sin 3t dt – y

A: Calculated integration and the applied laplace transformation in both sides

Q: y'' + 4y = cos2t y(0) = -2 and y'(0) = 0 Solve the IVP using the Laplace Transform.

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Q: y” − 2y' + 5y 8e¯ª, y (0) ³, y (0) = 2, y’(0) = 12 =

A: It is known that: L{f(n)}=snF(s)−sn−1f(0)−sn−2f'(0)−⋯−sf(n−2)(0)−f(n−1)(0) Hence, it can be written…

Q: When the Laplace transform is used to solve the IVP: y' +5 y=314, y(0) = 2 1/4+ the following…

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Q: Use the Laplace transform to solve y' - v = te'sint, y(0) = 0

A: To solve the given IVP, first we take the Laplace transform of differential equation and then we use…

Q: Qi Write the order and degree of the given. ODE'S.check either these equations aye nón-linear. Also…

A: Consider the given function. y''+x2y-2y'=sinx As the maximum order of the derivative is 2.  So, the…

Q: f"(t)-4f(t)=sin2t where f(0)=1 and f'(0)=-2 Use the Laplace transform to solve the equation

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Q: Using Laplace Transform, solve the following initial value problem Зу' - 4y — sin 2t У) --

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Q: Solve the following ODE using Laplace Transform: 2. у"+2y' - 3у%3Dбе-3t y(0) = 0, y'(0) = 0

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