Solving a Differential Equation with Special Integrating Factor

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SUMMARY

The discussion focuses on solving the differential equation dy/dx = 2 + √(y - 2x + 3) using a special integrating factor. Participants express difficulty in applying traditional methods such as separation of variables, exact equations, and Bernoulli equations. A suggested approach involves the substitution v = y - 2x + 3 to simplify the equation before applying special integrating factors. This method is presented as a straightforward solution to the problem at hand.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with methods such as separation of variables and exact equations
  • Knowledge of Bernoulli equations
  • Concept of integrating factors in differential equations
NEXT STEPS
  • Research the method of special integrating factors in differential equations
  • Learn about substitution techniques in solving differential equations
  • Study the application of change of variables in differential equations
  • Explore examples of solving differential equations using integrating factors
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Students and educators in mathematics, particularly those studying differential equations, as well as anyone seeking to enhance their problem-solving skills in this area.

kuahji
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dy/dx=2+[tex]\sqrt{y-2x+3}[/tex]

The only way we've been taught to solve differential equations so far is, separation of variables method, exact equation, bernoulli equation, homogeneous, and we're about to start special integrating factor.

I can't seem to get the equation into any of the first forms listed. Which leads me to believe its a special integrating factor problem. Or am I incorrect in this assumption?
 
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kuahji said:
dy/dx=2+[tex]\sqrt{y-2x+3}[/tex]

The only way we've been taught to solve differential equations so far is, separation of variables method, exact equation, bernoulli equation, homogeneous, and we're about to start special integrating factor.

I can't seem to get the equation into any of the first forms listed. Which leads me to believe its a special integrating factor problem. Or am I incorrect in this assumption?

I would say try substitution v = y-2x
 
Why don't you try a change of variable v=y-2*x+3 before resorting to extreme measures? It looks dead simple to me.
 

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