Question

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)=

Answer #1

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...

Solve the initial value problem
x′=x+y
y′= 6x+ 2y+et,
x(0) = 0, y(0) = 0.

Consider the following initial value problem: dx/dt + 7x/t =
et^4, x(1) =2
(a) Find an integrating factor for the differential
equation.
(b) Use the integrating factor to solve the initial value
problem

Solve the initial value problem.
x'=x+2y
y'=7x+y
with inition contitions x(0)=2 and y(0)=4.

Solve the initial value problem. 5d^2y/dt^2 + 5dy/dt -
y = 0; y(0)=0, y'(0)=1

dy/dt=x , dx/dt=6x-8y, x=1 and y=-1 when t=0

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

For 2y' = -tan(t)(y^2-1) find general solution (solve for y(t))
and solve initial value problem y(0) = -1/3

Solve the initial value problem.
d^2y/dx^2= -3 csc^2 x; y' (pi/4)=0; y(pi/2)=0
The solution is y=____.

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

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