I can't remember what type of differential equation this is or how to solve it

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SUMMARY

The differential equation discussed is of the form dA/dx = ab + kA, where k, a, and b are constants. The solution approach involves recognizing that the equation can be manipulated into a separable form. By multiplying both sides by dx/(ab + kA), the equation can be integrated, leading to an exponential solution. The key insight is identifying the integral of functions like 1/(x+1) to solve the equation effectively.

PREREQUISITES
  • Understanding of differential equations, specifically separable equations.
  • Knowledge of integration techniques, particularly integrating rational functions.
  • Familiarity with constants in differential equations and their implications.
  • Basic algebraic manipulation skills to rearrange equations.
NEXT STEPS
  • Study the method of separation of variables in differential equations.
  • Learn integration techniques for rational functions, focusing on forms like 1/(x+c).
  • Explore exponential functions and their applications in solving differential equations.
  • Review examples of differential equations with constant coefficients for deeper understanding.
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Students studying differential equations, educators teaching calculus, and anyone looking to enhance their problem-solving skills in mathematical analysis.

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Homework Statement


I have a differential equation of the form:
dA/dx = ab + kA

and I need to solve it


Homework Equations





The Attempt at a Solution


I've started it by moving the right hand side of the equation to the bottom of the left hand side and the bottom of the left to the right. I can recognise that this will probably take the form of an exponential in the final answer, but I can't see how you get to that as the bottom of the l.h.s isn't a simple function of A. How do I go about solving this kind of DE? Is it the same as if it didnt have the constant terms in it?
 
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Are k,a, and b constants?...If so your equation is separable...just multiply both sides by dx/(ab+kA)...what do you see?
 
Yeah I think I worked out how to do it on my walk home from uni - I think I'd forgotten how to integrate functions of the type 1/(x+1) which I can now see it is!
 

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