Question

Consider the following initial value problem: dx/dt + 7x/t =
e^{t^4}, x(1) =2

(a) Find an integrating factor for the differential equation.

(b) Use the integrating factor to solve the initial value problem

Answer #1

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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)=

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...

dx/dt - 3(dy/dt) = -x+2
dx/dt + dy/dt = y+t
Solve the system by obtaining a high order linear differential
equation for the unknown function of x (t).

1) Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1
Let af/ax = (x + y)2 = x2 + 2xy +
y2.
Integrate each term of this partial derivative with respect to
x, letting h(y)
be an unknown function in y.
f(x, y) = + h(y)
Find the derivative of h(y).
h′(y) =
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt...

Solve the Initial Value Problem:
a) dydx+2y=9, y(0)=0 y(x)=_______________
b) dydx+ycosx=5cosx,
y(0)=7d y(x)=______________
c) Find the general solution, y(t), which solves the problem
below, by the method of integrating factors.
8t dy/dt +y=t^3, t>0
Put the problem in standard form.
Then find the integrating factor, μ(t)= ,__________
and finally find y(t)= __________ . (use C as the unkown
constant.)
d) Solve the following initial value problem:
t dy/dt+6y=7t
with y(1)=2
Put the problem in standard form.
Then find the integrating...

1)Consider the following initial-value problem.
(x + y)2 dx + (2xy + x2 − 2) dy =
0, y(1) = 1. Let af/ax = (x + y)2 =
x2 + 2xy + y2. Integrate each term of this
partial derivative with respect to x, letting
h(y) be an unknown function in y.
f(x, y) = + h(y)
Solve the given initial-value problem.
2) Solve the given initial-value problem.
(6y + 2t − 3)
dt + (8y + 6t
− 1) dy...

Solve the following autonomous differential equation with the
given initial condition.
dx/dt=8-4x, where x(1)=-7
x=?

dx/dt=(1/4)x^3 -x,
c(0)=1
compute the solution to this initial value problem. An
algebraically implicit solution for x(t) is acceptanle
x(0)=1

Solve the initial-value problem.
x' + 7x =
e−7t
cos(t),
x(0) = −1
x(t) =

Solve the initial value problem 9(t+1) dy dt −6y=18t,
9(t+1)dydt−6y=18t, for t>−1 t>−1 with y(0)=14. y(0)=14. Find
the integrating factor, u(t)= u(t)= , and then find y(t)= y(t)=

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