## Friday, March 27, 2015

### Separation of Variables, 24

Category: Differential Equations

"Published in Newark, California, USA"

Find the general solution for

Solution:

Consider the given equation above

Divide both sides of the equation by cos x sin y, 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

## Thursday, March 26, 2015

### Separation of Variables, 23

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

Multiply both sides of the equation by dx, we have

Since both sides of the equations are already factored according to their variables, then we can separate the other variables from dy and dx as follows

Integrate on both sides of the equation, we have

Therefore, the general solution is

where D = 1/C.

## Wednesday, March 25, 2015

### Eliminating Arbitrary Constant, 25

Category: Differential Equations

"Published in Newark, California, USA"

Eliminate the arbitrary constant for

Solution:

Consider the given equation above

Take the derivative on both sides of the equation with respect to x, we have

Take the derivative on both sides of the equation with respect to x, we have

Multiply the first derivative equation by -2 and add it to the second derivative equation, we have

---------------------------------

Substitute the value of c1 to the second derivative equation, we have

Substitute the values of c1 and c2 to the given equation and therefore, the final answer is