Solving differential equations

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SUMMARY

The discussion focuses on solving the differential equation dy/dx = 3x²y. Participants suggest using the method of separation of variables to find the general solution. By rearranging the equation to isolate y on the left-hand side and dx on the right-hand side, users can set up two integrals for further analysis. This approach leads to a clearer path toward obtaining the solution.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with separation of variables technique
  • Basic integration skills
  • Knowledge of general solutions in calculus
NEXT STEPS
  • Study the method of separation of variables in detail
  • Practice solving first-order linear differential equations
  • Explore integration techniques for various functions
  • Learn about the existence and uniqueness theorem for differential equations
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Students studying calculus, mathematicians focusing on differential equations, and educators teaching advanced mathematics concepts.

wezzo62
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Find the general solution to: dy/dx = 3x2y

I tried saying u = 3x2 and v = y
then du/dv = 6x and dv/dy = 1

and get 3x2 + 6xy but now i think iv gone completely the wrong way around this . . . .
 
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Try using separation of the variables.
 
wezzo62 said:
Find the general solution to: dy/dx = 3x2y

I tried saying u = 3x2 and v = y
then du/dv = 6x and dv/dy = 1

and get 3x2 + 6xy but now i think iv gone completely the wrong way around this . . . .

You can swing the y over to the left hand side (LHS) of the equation, and the dx to the RHS.
This gives you two integrals. Do them, and see what happens.
 

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