2. y" — у %3D 4 cost у (0) — 0 y'(0) = 1

Q: (c) Use the Laplace transform to solve the following IVP y -2y -3y = e cos(t) y (0) = y(0) = 0.

A: The objective here is to solve the given differential equation using Laplace transform: Given…

Q: Solve the initial value problem using Laplace transform y" – 4y'+4y= 3te", y(0)=4, y'(0) = 2

A: The given question is related with Laplace transform. Given that,                    y'' - 4y' + 4y…

Q: f (t)%3 3e ' cosh ( In 2r)

A:

Q: use the laplace transform to solve

A: Hi! As per norm we will be answering only the first question since both of the solutions are long.…

Q: f(d) = e-2d d4

A:

Q: SET UP AND INTEGRATE AND GET TO THE FINAL RESULT FIND THE LAPLACE TRSNSFORM OF THE GIVEN FUNCTION…

A:

Q: 3. Use definition (not tables) of L{f(t)}= [ e"f (t)dt to find L{1*e" } . Assume s>9

A:

Q: t3 - 3t2 + 5t – 8

A:

Q: 2.) у" - Зу' — 2у %3D0 У (0) %3D0, у'(0) %3D 9 ,у" %3D0

A:

Q: Obtain the F(s) of the following f(t) 1. f(t) = } (-1 0st<1 ={'1 t21

A: we have given the function f(t)=-1  , 0≤t&lt;1  1  ,    t≥1 we have to find the Laplace…

Q: #o5 Selve the simultem Eou) equatis m3 using ん·T. プ=1; (()=onx() ナ? -0;1()=y() dt

A:

Q: Solve the equation subject to the given conditions. d'y dy dx² dx 6y=4, y(0)=3, y'(0)=2

A:

Q: 2x" - 3x' + x = 0 x(0) = 2, x'(0) = −1

A:

Q: 5 sinh (3t) +4 cosh (3t)

A:

Q: y"+2"-z' = 0 y' + z 221-ex - Yo = 0, y = 1 20= 1, 2 = 1

A:

Q: Find Lf" sin /6t-r'e"}

A: Please see below

Q: F(s) = 1 (s + 1)²(s² + 4)

A:

Q: X f(x) 0,0 0,5 1,0 2,119 1,0 15 20 2,910 3945 5,72 2,5 8,695

A:

Q: 8. Solve using Laplace transform: y" + 2y – 3y = 8e¬t + 8 (t – ), y(0) = 3, y' (0) = –5.

A:

Q: Solve the given symbolic initial value problem. у'+ 9y'+ 20y 3D е ""6(t-3); у(0) 3 2, у'(0)%3 - 9…

A: We have to solve the given differential equations using Laplace transform.

Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

A:

Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

A:

Q: x" (t) – x' (t) = te*, x (0+) = 1, x' (0+) = 0. --

A:

Q: f (t) = t?cos3t

A:

Q: Find the Laplace transform of the following signal which is periodic with period 20. 20 15 20 t -201

A:

Q: Q18: y′ − 2y + [y(2) dz=e², y(0) = 0.

A: The given equation is         y' - 2y + ∫0tyzdz = et  . . . . . . (1)     With condition y(0) = 0 .…

Q: According to Kirchoff's voltage law, the sum of the voltage drops across these elements is equal to…

A: