Category: Differential Equations, Integral Calculus
"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 term is a 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
Therefore, the general solution is
Category: Differential Equations, Integral Calculus
"Published in Newark, California, USA"
Find the general solution for
Solution:
Consider the given equation above
Transpose xy to the right side of the equation, we have
Arrange the above equation by separation of variables, we have
Integrate on both sides of the equation, we have
Take the inverse natural logarithm on both sides of the equation
where K = eC. Therefore, the general solution is
Category: Differential Equations, Integral Calculus
"Published in Newark, California, USA"
Find the general solution for
Solution:
Consider the given equation above
The
given equation is a 3rd Order Differential Equation because the third
derivative of y with respect to x is involved. We can rewrite given
equation as follows
Multiply both sides of the equation by dx, we have
Integrate on both sides of the equation, we have
Rewrite the above equation as follows
Multiply both sides of the equation by dx, we have
Integrate on both sides of the equation, we have
Multiply both sides of the equation by dx, we have
Integrate on both sides of the equation, we have
where B = ½ C1. Therefore, the general solution is
