Category: Differential Equations
"Published in Newark, California, USA"
Find the general solution for
Solution:
Consider the given equation above
Express y' as dy/dx as follows
By separation of variables, transpose dx to the right side of the equation and y to the left side of the equation, we have
Integrate on both sides of the equation, we have
Take the inverse natural logarithm on both sides of the equation, we have
Therefore, the general solution is
Category: Differential Equations
"Published in Newark, California, USA"
Find the general solution for
Solution:
Consider the given equation above
Express y' as dy/dx as follows
By separation of variables, transpose dx to the right side of the equation and cos y to the left side of the equation, we have
Integrate on both sides of the equation, we have
In
this type of integration of trigonometric functions, we need to use the
principles of trigonometric identities first before we can do the
simple integration of trigonometric functions. Hence, the above equation
becomes
Therefore, the general solution is
where A = 4C.
Category: Differential Equations
"Published in Newark, California, USA"
Find the general solution for
Solution:
Consider the given equation above
Since the given equation is already arranged according to their variables, then we can integrate on both sides of the equation as follows
In this type of integration of trigonometric functions, we need to use the principles of trigonometric identities first before we can do the simple integration of trigonometric functions. Hence, the above equation becomes
Therefore, the general solution is
where D = 3C.
