- #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
Click For Summary
Homework Help Overview
The problem involves solving a differential equation of the form y'=(xy-y^2)/x^2, which is related to differential equations and variable separation techniques.
Discussion Character
- Exploratory, Mathematical reasoning
Approaches and Questions Raised
- The original poster attempts to manipulate the equation by substituting variables and expressing y' in terms of z. Some participants suggest rearranging terms for integration, while others discuss the need to separate variables effectively.
Discussion Status
Participants are actively discussing the next steps for integration and variable separation. Guidance has been offered regarding the manipulation of terms, but there is no explicit consensus on the approach to take next.
Contextual Notes
There appears to be some confusion regarding the integration process, as indicated by requests for clarification from the original poster.
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
- 38,109
- 10,671
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
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