Category: Differential Equations
"Published in Vacaville, California, USA"
Find the general solution for
Solution:
Consider the given equation above
Did
you notice that the given equation cannot be solved by separation of
variables? A trigonometric function is a combination of x and y in the function and
there's no way that we can separate x and y.
This
type of differential equation is a homogeneous function. Let's consider
this procedure in solving the given equation as follows
Let
so that
Substitute the values of y and dy to the given equation, we have
The resulting equation can now be separated by separation of variables as follows
Integrate on both sides of the equation, we have
Take the inverse natural logarithm on both sides of the equation, we have
But
Hence, the above equation becomes
Therefore, the general solution is
Category: Differential Equations
"Published in Vacaville, California, USA"
Find the general solution for
Solution:
Consider the given equation above
In order to separate dx and dy from other variables, divide both sides of the equation by x√1 + y² as follows
Integrate both sides of the equation, we have
Take the inverse natural logarithm on both sides of the equation, we have
Therefore, the general solution is
Category: Differential Equations
"Published in Newark, California, USA"
Find the general solution for
Solution:
Consider the given equation above
Did
you notice that the given equation cannot be solved by separation of
variables? The first and second term are the combination of x and y in the group and
there's no way that we can separate x and y.
This
type of differential equation is a homogeneous function. Let's consider
this procedure in solving the given equation as follows
Let
so that
Substitute the values of y and dy to the given equation, we have
The resulting equation can now be separated by separation of variables as follows
Integrate on both sides of the equation, we have
But
Hence, the above equation becomes
where D = 2C.
Therefore, the general solution is
