Question

you must establish a definition on differential equation and
denote with an example where it is not possible to identify it as
such.

Answer #1

Find the general solution of the following differential
equation. Primes denote derivatives with respect to x.
y'=(289x+y)^2

Find the general solution of the following differential
equation. Primes denote derivatives with respect to x.
(x+3y)y'=8x-y

Find the general solution of the following differential
equation. Primes denote derivatives with respect to x.
x(x+6y)y'=y(x-6y)

Where does the differential equation come from? Can you just
choose whichever one you please or is there something about the one
used?

I'm taking differential equation class now and I need some
example questions(and answer) about "Mixing Problem" and
"Second-Order Differential Equations". The question must be related
to reality.

The dependent variable y is missing in the given differential
equation. Proceed as in Example 1 and solve the equation by using
the substitution u = y'
y'' + (y' )2 + 1 = 0

Find the general solution of the differential equation
y′′ − 2y′ − 3y = ae3t, where a is a constant

Please provide an example of, and explain, solving a first order
linear differential equation using a power series

a. Solve the following differential equation, where r and ω are
constant parameters: dP/ dt = r(1 − cos(ωt))P
b. Solve the following differential equation: y'(x) + 4xy(x) =
2xe^(−x^ 2)

Set up a differential equation (with initial conditions!) and
solve the differential equation in order to answer the following
problem (you must also precisely explain what your variables x and
y represent prior to writing down any computations). You are a
police detective investigating a murder case. The first thing you
must determine for this case is the time of death. Here’s what you
know:
The body was found at 9:00pm and its temperature at that time
was 60°F. The...

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