Question

Initial value problem : Differential equations:

dx/dt = x + 2y

dy/dt = 2x + y

Initial conditions:

x(0) = 0

y(0) = 2

a) Find the solution to this initial value problem

(yes, I know, the text says that the solutions are

x(t)= e^3t - e^-t and y(x) = e^3t + e^-t

and but I want you to derive these solutions yourself using one of the methods we studied in chapter 4) Work this part out on paper to hand in.

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

dx/dt=y, dy/dt=2x-2y

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

Solve the system of equations by method of the Laplace
transform:
3 dx/dt + 3x +2y = e^t
4x - 3 dy/dt +3y = 3t
x(0)= 1, y(0)= -1

Solve the Initial Value Problem
(y2 cos(x) − 3x2y − 2x) dx + (2y sin(x) −
x3 + ln(y)) dy = 0, y(0) = e

solve the given initial value problem
dx/dt=7x+y x(0)=1
dt/dt=-6x+2y y(0)=0
the solution is x(t)= and y(t)=

Consider the initial value problem
dy dx
=
1−2x 2y
, y(0) = − √2
(a) (6 points) Find the explicit solution to the initial value
problem.
(b) (3 points) Determine the interval in which the solution is
deﬁned.

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 given system of differential equations by systematic
elimination. 2 dx/dt − 6x + dy/dt = e^t
dx/dt − x + dy/dt = 6e^t

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