Category: Differential Equations
"Published in Newark, California, USA"
Find the particular solution for
in which y = 0 when x = 0.
Solution:
Consider the given equation above
In order to separate dx and dy from other variables, divide both sides of the equation by as follows
Integrate both sides of the equation, we have
Substitute the value of x and y in order to get the value of C as follows
Therefore, the particular 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)
Saturday, August 2, 2014
Friday, August 1, 2014
Homogeneous Functions - Arbitrary Constant, 4
Category: Differential Equations
"Published in Newark, California, USA"
Find the particular solution for
in which y = 2 when x = 4.
Solution:
Consider the given equation above
Did you notice that the given equation cannot be solved by separation of variables? The algebraic functions 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
Substitute the value of x and y in order to get the value of C as follows
Therefore, the particular solution is
"Published in Newark, California, USA"
Find the particular solution for
in which y = 2 when x = 4.
Solution:
Consider the given equation above
Did you notice that the given equation cannot be solved by separation of variables? The algebraic functions 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
Substitute the value of x and y in order to get the value of C as follows
Therefore, the particular solution is
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