(3 points each) Solve the following differential equations using Laplace Transforms. Not credit w...
PROBLEM 3: LAPLACE TRANSFORMS OF DIFFERENTIAL EQUATIONS Find Laplace transforms of the following differential equations: a) y(t)+5y(t)-0 y(0)=2 b)2 +)0 y(o)- A: y(0)- B
use Laplace transforms to solve the given system of
differential equations
ponts) 6)) Use Laplace transforms to solve the system dc y = 2x-2y dt.dt dx _ ay = x - y dt at x(O) = 1, y(0) = 0
Solve the system of equations with Laplace Transforms:
(differential equations)
all parts please
Solve the system of equations with Laplace Transforms: x' + y' = 1, x(0) = y(0) = x'(0) = y'(0) = 0. y" = x' Let X(s) = LT of x(t) and Y(s) = LT of y(1). First obtain expressions for X(s) and Y(s) and list them in the form ready for obtaining their inverses. a. Y(s) = X(s) = %3D b. Now obtain the inverse transforms....
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Solve the following system of differential equations by using
Laplace transforms.
with x(0) = 0, x'(0) = 2, and y(0) = 0.
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dr 22 +3 + 3y = 0 d2dt dx2 + 3y = tet
Detailed answer using the Laplace Transforms method
Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0 . s?...
Sheet1 Control 1. Solve the following differential equations using Laplace transforms. Assume zero initial conditions dx + 7x = 5 cos 21 di b. + 6 + 8x = 5 sin 31 dt + 25x = 10u(1) 2. Solve the following differential equations using Laplace transforms and the given initial conditions: de *(0) = 2 () = -3 dx +2+2x = sin21 di dx di dx di 7+2 x(0) = 2:0) = 1 ed + 4x x(0) = 1:0) =...
K1=10, k2=7. Please do both
3) Using Laplace transforms, solve the following differential equations with the initial conditions indicated. Sketch the resulting functions of time dy 0, with y(O) - k2 bk2)+ kik20, with z(0) - 0, t( 2 dt2
Question 3
1. Sol orms to solve the following differential equations: 11se Laplace transforms to 47'(t) + 4y(t) = 9e' with y(0) = y(0) = 0. x) = 5 sin 2t with y(0) = 0 and y'(0) = 1. 2. y"(t) + 4y'o 3. y" (t) – 4v
Detailed answer with another method then the Laplace
transforms
Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0...
Q4. Laplace Transforms a) (20 points) Solve the differential equation using Laplace transform methods y" + 2y + y = t; with initial conditions y(0) = y(O) = 0 |(s+2) e-*) b) (10 points) Determine L-1 s? +S +1