The initial value problem y" + 4y" + y' - 6y = -12, y(0) = 1, y'(0) = 4, y"(0) = -2 is given. If the Laplace transform of y(t) is Y(S), first find Y(S). Then using Y(s) find the solution of the given initial value problem. s3 + 8s? + 15s + 12 A. Y(S) =- s4 + 4s3 + s? - 6s · y(t) = e* - e-* - 3e2t + 2 s3 + 8s? + 15s - 12 s4+ 4s3 + s2 - 6s O B. Y(S) = - y(t) = e* - e-* - 3e + 2 s3 + 8s2 - 15s - 12 s4+ 4s3 + s2 - 6s O C. Y(S) =- y(t) = et + et. 3e-2 +2 53 + 8s2 + 15s - 12 D. Y(s) = · y(t) = et + e-* - 3e-t + 2 s + 4s3 + s2 - 6s

Q: Solve the differential equation using Laplace Transform. (b) y" – y" + 4y' – 4y = 10e-t, y(0) = 5,…

A: We will find out the required solution.

Q: 1. Solve the following initial value problem using the Laplace Transform Method. y" + 4y + 4y = e…

A:

Q: 9. Use the method of Laplace transform to solve the initial value problem y/" + B*y = (a² + 3?)eat,…

A:

Q: Use the Laplace transform method to solve the initial value problem y\\ - 3y + 2y = 4e²t given that…

A: The given initial value problem  and and .The aim is to solve the IVP using the Laplace…

Q: When the Laplace Transform is applied to the initial value problem y"-2y + y =t + 2e" sin t cost ,…

A:

Q: Q3) Solve the following initial value problems by Laplace transform. (Show all details): A. y' +4y 0…

A:

Q: Solve thee IVP y" – 4y" – 9 y' +36y=0, y(0) = 1, y'(0) = 0, y"(0) = –1 by using Laplace…

A:

Q: 3. Use the Laplace transform method to solve the initial value problem r = 6x1 + 11r2, r = -4x1 –…

A:

Q: Q.4/ Find the inverse Laplace transform of given F(s) s2 +1 F(s) s(s + 1)2

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: The initial value problem y" - y" + y' -y = 0, y(0) = 1, y'(0) = 1, y"(0) = 3 is given. If the…

A:

Q: Solve the differential equation using Laplace Transform. (a) y" – 2y' + 5y = 8e'sin2t, y(0) = 1,…

A: a. The given differential equation is                                     y''-2y'+5y=8etsin2t   ,…

Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the…

A: Given function is: fγ,p,t=e-γtsinpt0t>0t<0 It is a form of the step function which is…

Q: Q3. Solve uring SVP y" - 5y¹ - 14y = Lapbre transform. the 9+ ult-3), y(u) = 0, y ! (o) = 10.

A:

Q: 1. Apply the Laplace transform to then system of differential equations. Write the resulting system…

A:

Q: Q3. Use the Laplace transform to solve the initial value problem (4) y" - 8y' + 15y = 9te²t, y (0) =…

A: Since you have posted a multiple question according to guildlines I will solve first(Q3)   question…

Q: (i) y"-10y'+9y=5t, y(0)=-1, y'(0)=2

A: As you asked more than one question I solved the first one.

Q: Use the Laplace transform to solve the following initial value problem: y' + 8y = 0 y(0) = 3, y(0) =…

A:

Q: Consider the following initial value problem. у" + 8y' + 25y %3D 8(t — п) + 8(t - 7л), у(0) 3D 1,…

A:

Q: Consider the variable coefficient linear non-homogeneous ODE where and where u and are unknown…

A: The given problem is to find the values of u' and v' for the which the particular solution yp =…

Q: 10. Use the method of Laplace transform to solve the initial value problem ý (0) = aa +bB. y" - 2ay'…

A: We have to solve the given problem using the method of Laplace transform.

Q: Given the difference equation y(n + 2)- y(n + 1)- vln)=x(n), n20 [1, n20 with x(n)= and initial…

A: Given: To apply z transform to both sides of the equation and find the expression for Y(z)

Q: 5. Use the Laplace transform to solve the following system: Sx"+y" = e²t, (2x' + y" = −e²t, x(0) =…

A:

Q: Evaluate equation y’ – 3y' – 4y = e³x using the Laplace transform, with initial conditions y(0) = -5…

A:

Q: Consider the initial value problem y" - 2y' – 7y = 12t y(0) = 8, y'(0) = 4 A. Use the Laplace…

A:

Q: The initial value problem y" + 5y" - 8y' - 12y = -48, y(0) = 8, y'(0) = 29, y"(0) = -83 is given. If…

A: The solution is given as solution:-we have-y'''+5 y''-8 y'-12y=-48 ......1and y(0)=8, y'(0)=29,…

Q: Solution the the following initial value problem using the Laplace transform y" + 4y = 4t, y(0) = 1,…

A: Given: Given initial value problem is y''+4y=4t, y0=1,y'0=5 We find solution by using the Laplace…

Q: y" +16y= cos(41) 7. Solve the initial value problem (0) =1 (0)=1 using the Laplace transform. No…

A:

Q: y' -y = t et sint, y(0) = 0

A: The answer is given by using properties of Laplace transform.

Q: 9. Use the method of Laplace transform to solve the initial value problem y" + B²y = (a² + 3²) eat,…

A:

Q: 5. 2y"+3y"-3y'– 2 y = e',

A:

Q: 27 20 Y()=0, YOX=5 Use laplace transform to Solve the initial value problem: y" +9y=68 (+-5) y (0) =…

A:

Q: This question is about the variation of parameters we talked in class. The following parts will help…

A: Since you have posted multiple question but according to guidelines we will solve first question for…

Q: Consider the initial value problem dy d²y dy dt2 dt +10. +41y=-7e5t cos(5t), y(0) = -7, ,dt -(0) -4…

A: Step 1:  Y(s) Partial Fractions:The equation can be rewritten to isolate Y(s): (s2 + 10s + 41) Y(s)…

Q: Consider the initial value problem y′+3y=18t, y(0)=4. 2 - Solve your equation for Y(s)=…

A: Solution:Given initial value problem: we have to solve the given initial value problem by using…