Category: Differential Equations
"Published in Vacaville, California, USA"
Find the particular solution for
in which y = 3 when x = 1.
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
There's another way in getting the particular solution of the given equation above 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)
Thursday, July 31, 2014
Wednesday, July 30, 2014
Separation of Variables - Arbitrary Constant, 3
Category: Differential Equations
"Published in Newark, California, USA"
Find the particular solution for
in which y = 6 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 (y - 2) cot x as follows
Integrate both sides of the equation, we have
Take the inverse natural logarithm on 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
"Published in Newark, California, USA"
Find the particular solution for
in which y = 6 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 (y - 2) cot x as follows
Integrate both sides of the equation, we have
Take the inverse natural logarithm on 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
Tuesday, July 29, 2014
Separation of Variables - Arbitrary Constant, 2
Category: Differential Equations
"Published in Newark, California, USA"
Find the particular solution for
in which y = 2 when x = 5.
Solution:
Consider the given equation above
Since dx and dy have the same variables, then we can integrate both sides of the equation as follows
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 = 5.
Solution:
Consider the given equation above
Since dx and dy have the same variables, then we can integrate both sides of the equation as follows
Substitute the value of x and y in order to get the value of C as follows
Therefore, the particular solution is
Subscribe to:
Posts (Atom)