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Solving Equations - Homogeneous Functions, 9

__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
Take the inverse natural logarithm on both sides of the equation, we have
But
Hence, the above equation becomes

where D = C².
Therefore, the general solution is