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

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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.
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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