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## Main Question or Discussion Point

We were looking at some examples of systems of differential equations in class a couple days ago, and some of them were simple looking systems. One such was

##\frac{dr}{dt} = 4j##

##\frac{dj}{dt} = r##

Why is it that we can't treat this as a scenario where both sides of each equation could just be integrated immediately or something like in physics where the first equation would become ##dr = 4jdt## and then integrate? (I have a question current posted in the calculus section about splitting the derivative if anyone cares to answer when this technique DOES work)

##\frac{dr}{dt} = 4j##

##\frac{dj}{dt} = r##

Why is it that we can't treat this as a scenario where both sides of each equation could just be integrated immediately or something like in physics where the first equation would become ##dr = 4jdt## and then integrate? (I have a question current posted in the calculus section about splitting the derivative if anyone cares to answer when this technique DOES work)