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 2nd Order Differential Equation because the second 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
Multiply both sides of the equation by dx, we have
Integrate on both sides of the equation, we have
but
Hence, the above equation becomes
where B = C1 - 1.Therefore, the general solution is
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
