(b) Use the Laplace transform method to find the solution of d²y 6+9y= 4e", yo = 2, y1 = 0. dt dy %3D

Q: solve: y" - Hý + 4y = 40st; y(0)=2₁ y(0)=5 using Laplace transform

A: y''-4y'+4y=4cos 2t Taking Laplace transform on both…

Q: Solve the equation using Laplace transform y" - 6y' +9y t²e³t, y(0) = 2, y'(0) = 6. =

A: Introduction: There are many different ways that are applied to solve an initial value problem. One…

Q: find the a general solution to dy/dt = {{-9,12},{6,-8}}y

A: (.)  Given ,            (.)  Consider a system of differential equation ,…

Q: (x' = x- 2y V = 5x – yi x(0) = -1, y(0) = 2. %3D %3D %3D %3D

A:

Q: Integrate the function. S dt o. O. V6-R+ sin'1 6t + C 6t o. + C 612 o. 6t 16-12

A: We can find the integral as below.

Q: + y = ty dt

A:

Q: Draw the bifurcation diagram for dy/dt = y(a-y)

A: We can use concept of critical points in order to solve the given problem.

Q: J(2t-3)-e-t²,3t i. 2t – dt 3 2vlnx dx . ii. X 2 iii. (2y-3]12 kdy.

A:

Q: d2y/dt2+a2y=b sin wt  ( laplace transform )

A:

Q: Use Raplace Transform to Solue y?+3y'+2y=DUglt) O and %3D guen ylo) =0 y'l6)=1 %3D

A: Use Laplace table to solve this.

Q: y"+2ў-15y=0 усо)=1 y'(0)=-2

A:

Q: (2t – 3)·e -t²+3t dt 3 2/Inx dx . X (2у-3)12

A:

Q: ý + 16y = 8 (t – ) sin (2t), y(0) = 0, ÿ(0) = 0

A: The solution is given by using some formulas of Laplace transform as follows :

Q: 4. a) Find the general solutions of the following differential equations. Express the general…

A:

Q: Use Laplace Transform to solue y' +zy y=4et %3D given ylo)"= 2 and y'lo). y'66)=-1 %3D

A:

Q: Determine whether the given equation is separable, linear, neither or both.  (t^2+1)dy/dt=yt-y

A: