All Questions
4
questions
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Trouble getting the same answer as the textbook (separable first order differential equation)
I was trying to resolve the following differential equation:
$$ y'=e^x(y+1)^2$$
where $y = y(x)$
and I start to resolve it using the following steps:
first we find the solution for when $(y+1)^2=0$ ...
0
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2
answers
298
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Is $y(x)=0$ a solution to the differential equation, $y=y'$?
I think I read or was told that the natural exponential function, $e^x$ is the only solution to $y=y'$, and that it originally was defined by that property.
But isn't $y(x)=0$ one too?
If so, $e^x$ ...
0
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2
answers
78
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Find a function $f$ such that $\int_0^{P(x)} f(t) dt = 1- e^{2P(x)}$
I'm trying to solve the following homework problem. It states as follows:
"Let $P(x)$ be a polynomial such that $P'(x) \neq 0$ for all values of $x$. Does there exist a continuous function $f$ such ...
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2
votes
4
answers
107
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Analytically determine if $f(x) = f'(x)$ is possible?
I was taking a test and two true/false type questions were asked.
In one of them, I had to say if there is a function $f(x)$ such that $f(x) = f'(x)$. Of course, $e^x$ is such a function and almost ...
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