Separable Differential Equations
This section is an essential method for solving differential equations. Especially about the initial condition
, it is the critical information for getting the original function.
Example
No we can't. Because:
Example
First to transfer same terms to the same side.
Then take integral of each side
Operate to get
y
Example
We could easily get the derivative of second equation is
y' = -2/3
.Let's see if two of the derivatives are equal by substitute back the
y
expression:Clearly they're equal. So the answer is
YES
.
Example
Move the same terms to each side:
Take integral of both side:
Get that:
Plug in
y(0) = 3
to getC=4
, so the equation then be:Set
y=1
and gett = ln(1/2) = -ln(2)
Exponential model equations
►Jump to Khan academy for practice
►Refer to Khan academy: Worked example: exponential solution to differential equation
Example
Rewrite the equation, and take integral of both side:
And we get:
Let's plug in
g(3)=2
to solve forC
:Take
C
back and get the equation forg(x)
:
Example
We are told that the rate of change of P is proportional to P, which means in Math is:
It's clear that is a
Differential Equation
, and we rewrite them and take integral of both side to get:Solve for
C
:Solve for
k
:get the
k
:Now we have the full equation, and get the result:
Last updated