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

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The differential equation dy/dx=3y can be solved by separating variables, leading to y'/y=3. The integration of this equation results in the natural logarithm, but the correct approach is to recognize that the solution takes the form y=Ce^(3x). Travis initially struggled with the integration process but ultimately found the solution. The discussion highlights the importance of understanding separation of variables and exponential functions in solving first-order linear differential equations.
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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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