- #1
sedaw
- 62
- 0
Homework Statement
y`=(xy-y^2)/x^2
The Attempt at a Solution
y` = y/x -(y/x)^2
{y/x=z , y=zx , y`=z+xz`}
-z^2=x*dz/dx
-z^2dx = xdz
what`s next ?
TNX .
Solving a Differential Equation with Variables and Steps | Math Homework Help
- Thread starter sedaw
- Start date
In summary, a differential equation is a mathematical equation that uses derivatives to describe the relationships between variables in a system. There are two main types: ordinary differential equations (ODEs) and partial differential equations (PDEs). They are widely used in various fields of science to model and analyze systems, such as population growth and heat transfer. Differential equations have many applications, including predicting weather and designing circuits. However, not all differential equations can be solved analytically and may require numerical methods.
y`=(xy-y^2)/x^2
y` = y/x -(y/x)^2
{y/x=z , y=zx , y`=z+xz`}
-z^2=x*dz/dx
-z^2dx = xdz
what`s next ?
TNX .
- #2
Mark44
Mentor
- 37,621
- 9,850
Next is to move the -z^2 and x factors around so they are with, respectively, dz and dx. Then integrate.
- #3
AUMathTutor
- 498
- 0
To integrate that, you need your z's on one side and your x's on the other. Dividing through by x*z^2 should do the trick.
- #4
sedaw
- 62
- 0
can u write can't understand .
TNX .
TNX .
- #5
sedaw
- 62
- 0
it`s o k .
TNX
TNX
1. What is a differential equation?
A differential equation is a mathematical equation that relates an unknown function to its derivatives. It involves the use of derivatives to describe and model the relationships between different variables in a system.
2. What are the types of differential equations?
The two main types of differential equations are ordinary differential equations (ODEs) and partial differential equations (PDEs). ODEs involve only one independent variable, while PDEs involve multiple independent variables.
3. How are differential equations used in science?
Differential equations are used in many fields of science, including physics, biology, chemistry, and engineering. They are used to model and analyze various systems and phenomena, such as population growth, heat transfer, and motion of objects.
4. What are the applications of differential equations?
Differential equations have a wide range of applications, such as predicting the weather, designing electrical circuits, and analyzing chemical reactions. They are also used in fields like economics, medicine, and computer science.
5. Is it possible to solve any differential equation?
No, not all differential equations can be solved analytically. Some equations may have no solution, while others may require numerical methods to approximate a solution. However, many commonly occurring differential equations have known solutions.
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