- Express
yin terms ofxfor differential equationdy/dx=ylny
(I'm officially out of ideas again)
this post was submitted on 14 May 2024
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solution
Not sure if I'd have gotten this one without Cavy's hint, I'm pretty bad with differential equationsLet z = ln(y)
Then z = dy/dx / y
dy/dx / y is the derivative of ln(y)
So we have z = d/dx ln(y), or ln(y) = d/dx ln(y)
ln(y) is its own derivative - so we must have ln(y) = e^x, which implies y = e^(e^x)