__Category__: Differential Equations

"Published in Vacaville, California, USA"
Find the general solution for
__Solution__:
Consider the given equation above
Perform the algebraic operations and group according to their variables as follows
By separation of variables, transpose (1 - b cos θ) to the right side of the equation and r to the left side of the equation as follows
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 Vacaville, California, USA"
Find the general solution for
__Solution__:
Consider the given equation above
By separation of variables, transpose y to the right side of the equation and (4 + e^{2x}) to the left side of the equation as follows

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
where E = C²

__Category__: Differential Equations

"Published in Vacaville, California, USA"
Find the general solution for
__Solution__:
Consider the given equation above
By separation of variables, transpose dP to the right side of the equation and V to the left side of the equation as follows
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