Question

Solve the given initial-value problem. (x + 2) dy dx + y = ln(x), y(1) = 10 y(x) =

Give the largest interval I over which the solution is defined. (Enter your answer using interval notation.)

I =

Answer #1

1) Solve the given differential equation by finding, as in
Example 4 of Section 2.4, an appropriate integrating factor.
(14 − 20y +
e−5x)
dx − 4 dy = 0
2) Solve the given initial-value problem.
x dy/ dx + y = 2x + 1, y(1) = 9
y(x) =
Give the largest interval I over which the solution is
defined. (Enter your answer using interval notation.)
I =
please show steps

Consider the IVP (x^2 - 2x)dy/dx = (x-2)y + x^2, y(1)=-2. Solve
the IVP. Give the largest interval over which the solution is
defined.

1) Solve the given differential equation by separation of
variables.
exy
dy/dx = e−y +
e−6x −
y
2) Solve the given differential
equation by separation of variables.
y ln(x) dx/dy = (y+1/x)^2
3) Find an explicit solution of the given initial-value
problem.
dx/dt = 7(x2 + 1), x( π/4)= 1

Consider the initial value problem
dy/dx= 6xy2 y(0)=1
a) Solve the initial value problem explicitly
b) Use eulers method with change in x = 0.25 to estimate y(1)
for the initial value problem
c) Use your exact solution in (a) and your approximate answer in
(b) to compute the error in your approximation of y(1)

Solve the separable equation 3xy^2 dy/dx = x^2 + 1 given y(0)
=5
I am getting a general solution of cubed root
x2/2+ln|x|+3c1 when I enter the initial
conditions y(0)=5 the equation is undefined. How do deal with this?
What would the final answer be?
Thanks

(a) State the interval on which the solution to the differential
equation (x^2-1)dy/dx + ln(x+1)y = 4e^x
with initial condition y(2) = 4 exists. Do not attempt to solve the
equation.
ODE
SHOW ALL STEPS PLEASE.

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...

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...

1.Solve the following initial value problem
a) dy/dx= y2/(x-3), with y(4)=2
b) (sqrt(x)) dy/dx = ey+sqrt(x), with y(0)= 0
2. Find an expression for nth term of the
sequence
a) {-1, 13/24, -20/120, 27/720, ...}
b) {4/10, 12/7, 36/4, 108, ...}

Solve the 1st order initial value problem:
1+(x/y+cosy)dy/dx=0, y(pi/2)=0

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