Separation of Variables, 25

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 y³e^x2, we have 

Integrate on both sides of the equation, we have  

Therefore, the general solution is  

where A = -2C 

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 

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.