Solving Differential Equation: dy/dx=3y | Travis

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SUMMARY

The differential equation dy/dx=3y can be solved using separation of variables. The correct steps involve rewriting the equation as y'/y=3, leading to the integration of both sides. The solution to the equation is y=Ce^(3x), where C is a constant. This method confirms the solution provided in the textbook.

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Find the set of all solutions of the following differential equation

dy/dx=3y

I've gotten this far

y'=3y

y'/y=3

I feel like I'm forgetting a fundamental integration identity like,

y=ln(y'/y) <-- Not sure that is even correct.

I'm not sure. The book says the solution is y=Ce^3x. It makes sense, I'm just stuck somewhere between start and finish.

Any help?

Thanks,
Travis
 
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Solved it. Thanks.
 

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