Simple Differential Equation

  • Thread starter SteliosVas
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  • #1
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Homework Statement



The problem is Solve the following differential equation: dy/dx = 6*x*y/(3-x^2)

Homework Equations



Okay so I know the first step is integrating both sides and separating the variables

The Attempt at a Solution



So separating the variables and integrating I get integral of \int y*dy \ = integral of
\int (6x)/(3-x^2) \, dx

Using substation for the the x variable I get -3ln(-x^2+3) +c and for the y variable as just y(x).

Now after this what is the next step. Should i rewrite the log natural as 1/(x^2-3)^2?
 

Answers and Replies

  • #2
Simon Bridge
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Now after this what is the next step.
Stop - you are there. Put LHS = RHS.
for the y variable as just y(x).
But ##\int y\;dy \neq y##
 
  • #3
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Homework Statement



The problem is Solve the following differential equation: dy/dx = 6*x*y/(3-x^2)

Homework Equations



Okay so I know the first step is integrating both sides and separating the variables
Separate the variables first before integrating.
SteliosVas said:

The Attempt at a Solution



So separating the variables and integrating I get integral of \int y*dy \ = integral of
\int (6x)/(3-x^2) \, dx
Check your algebra. The left side is NOT y * dy.
SteliosVas said:
Using substation for the the x variable I get -3ln(-x^2+3) +c and for the y variable as just y(x).

Now after this what is the next step. Should i rewrite the log natural as 1/(x^2-3)^2?
You have a mistake in here as well.
 

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