Category: Differential Equations, Integral Calculus
"Published in Suisun City, California, USA"
Find the general solution for
Solution:
Consider the given equation above
The given equation can be written as
Arrange the above equation by separation of variables, we have
Integrate on both sides of the equation, we have
Therefore, the general solution is
You can also eliminate their fraction by multiplying both sides of the equation by their Least Common Denominator (LCD) which is 4 as follows
Note: A constant multiply by another constant or coefficient is still a constant.
Category: Differential Equations, Integral Calculus
"Published in Suisun City, California, USA"
Find an equation of a curve that passes thru the point (1, 1) and whose slope at (x, y) is y²/x³.
Solution:
The slope of a curve is a first derivative of the equation of a curve with respect to x. In this problem, the slope of a curve at (x, y) is written as
Arrange the above equation by separation of variables, we have
Integrate on both sides of the equation in order to get the equation of a curve as follows
To solve for the value of C, substitute the value of x and y which is the given point in the curve, as follows
Therefore, the equation of the curve is
Multiply both sides of the equation by their Least Common Denominator, which is 2x²y, we have
Therefore, the equation of a curve is
Category: Integral Calculus
"Published in Newark, California, USA"
Evaluate
Solution:
Consider the given equation above
The first thing that we have to do is to take out the coefficient as follows
Apply the integration by power formula, we have
Therefore, the answer is
where C is the constant of integration.
