Question

Solve the following differential equation using Laplace dy/dt +2y=12sin4t y(0) =10

Answer #1

Use the Laplace transform to solve the given system of
differential equations. dx/dt=x-2y dy/dt=5x-y x(0) = -1, y(0) =
6

Solve the system of differential equations using laplace
transformation
dy/dt-x=0,dx/dt+y=1,x(0)=-1,y(0)=1

1. Solve the following initial value problem using Laplace
transforms.
d^2y/dt^2+ y = g(t) with y(0)=0 and dy/dt(0) = 1 where g(t) = t/2
for 0<t<6 and g(t) = 3 for t>6

Use the Laplace transform to solve the given system of
differential equations. 2 dx/dt + dy/dt − 2x = 1
dx/dt + dy/dt − 6x − 6y = 2
x(0) = 0, y(0) = 0

Consider the differential equation y′′+ 9y′= 0.(
a) Let u=y′=dy/dt. Rewrite the differential equation as a
first-order differential equation in terms of the variables u.
Solve the first-order differential equation for u (using either
separation of variables or an integrating factor) and integrate u
to find y.
(b) Write out the auxiliary equation for the differential
equation and use the methods of Section 4.2/4.3 to find the general
solution.
(c) Find the solution to the initial value problem y′′+ 9y′=...

Solve the following system of differential equations:
dx/dt =x+2y
dy/dt =−x+3y

Write a matlab script file to solve the differential equation
dy/dt = 1 − y^3 with initial condition y(0)=0, from t=0 to t=10.
matlab question

Given the differential equation
y''−2y'+y=0, y(0)=1, y'(0)=2
Apply the Laplace Transform and solve for Y(s)=L{y}
Y(s) =
Now solve the IVP by using the inverse Laplace Transform
y(t)=L^−1{Y(s)}
y(t) =

Use the Laplace transform to solve the given system of
differential equations. dx dt = −x + y dy dt = 2x x(0) = 0, y(0) =
2

solve the differential equation
(2y^2+2y+4x^2)dx+(2xy+x)dy=0

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