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 3rd Order Differential Equation because the third
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
Rewrite the above 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
where
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
Multiply both sides of the equation by dx, we have
Integrate on both sides of the equation, we have
Consider
If
then
If
then
Hence, by integration by parts
Substitute the above equation to the original equation, we have
where
Category: Integral Calculus, Algebra
"Published in Newark, California, USA"
Evaluate
Solution:
Consider the given equation above
The first thing that we have to do is to integrate the given equation above, we have
The
constant of integration is not included in the definite integral.
Substitute the values of upper and lower limits to the above equation,
we have
Therefore,
