Category: Differential Equations
"Published in Newark, 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 (1 + y2)(1 + x2) as follows
Integrate both sides of the equation, we have
Apply the inverse trigonometric identities formula at the left side of the equation, we have
Take tangent on both sides of the equation, we have
where D = tan C.
Therefore, the general solution is
This website will show the principles of solving Math problems in Arithmetic, Algebra, Plane Geometry, Solid Geometry, Analytic Geometry, Trigonometry, Differential Calculus, Integral Calculus, Statistics, Differential Equations, Physics, Mechanics, Strength of Materials, and Chemical Engineering Math that we are using anywhere in everyday life. This website is also about the derivation of common formulas and equations. (Founded on September 28, 2012 in Newark, California, USA)
Tuesday, July 8, 2014
Monday, July 7, 2014
Solving Equations - Homogeneous Functions, 4
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
"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
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