First order differential qusetion [ ]

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SUMMARY

The discussion centers around solving a first-order differential equation using the method of separation of variables. The user successfully derived the equation 1/4 ln |1+2v| = ln|x| + C but seeks guidance on how to proceed with solving for v(x). The key relationship to utilize is v = y/x, which allows for substitution to find the solution to the differential equation.

PREREQUISITES
  • Understanding of first-order differential equations
  • Familiarity with the method of separation of variables
  • Knowledge of logarithmic functions and their properties
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the method of separation of variables in detail
  • Learn how to apply substitutions in differential equations
  • Explore the implications of the relationship v = y/x in solving differential equations
  • Practice solving first-order differential equations with various initial conditions
USEFUL FOR

Students studying calculus, particularly those focusing on differential equations, as well as educators looking for examples of solving first-order equations using separation of variables.

thomas49th
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First order differential qusetion [urgent]

Homework Statement


Question 7
HL2001.jpg



Homework Equations





The Attempt at a Solution


I can do part a)

and i can begin part b, using separation of variables I get:

1/4 ln |1+2v| = ln|x| + C

but how do i use this to solve equation I

Thanks :)
 
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Once you get v(x)

just substitute the known relationship v = y/x
 

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