differential equation - beginner question
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3
down vote
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If I have a differential equation on the form
$$y = y' cdot c_1$$
can I freely solve for $y'$ and use the solution for
$$y' = y cdot c_2$$
where $c_2 = frac{1}{c_1}$?
calculus differential-equations
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up vote
3
down vote
favorite
If I have a differential equation on the form
$$y = y' cdot c_1$$
can I freely solve for $y'$ and use the solution for
$$y' = y cdot c_2$$
where $c_2 = frac{1}{c_1}$?
calculus differential-equations
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
If I have a differential equation on the form
$$y = y' cdot c_1$$
can I freely solve for $y'$ and use the solution for
$$y' = y cdot c_2$$
where $c_2 = frac{1}{c_1}$?
calculus differential-equations
If I have a differential equation on the form
$$y = y' cdot c_1$$
can I freely solve for $y'$ and use the solution for
$$y' = y cdot c_2$$
where $c_2 = frac{1}{c_1}$?
calculus differential-equations
calculus differential-equations
edited 6 mins ago
asked 6 hours ago
gariban17
324
324
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add a comment |
1 Answer
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Yes, of course. Assuming that $c in mathbb R$ is a constant, then if $c neq 0$ :
$$y = y' cdot c Leftrightarrow y' = y cdot frac{1}{c} equiv y cdot c$$
Since $c$ is an arbitrary constant, any expression of it will also be a constant, so you can always "manipulate" it to be just $c$. Note that only if you have some certain restrictions for $c$, then you will need to take these in mind on how they affect the expression $1/c$.
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
7
down vote
accepted
Yes, of course. Assuming that $c in mathbb R$ is a constant, then if $c neq 0$ :
$$y = y' cdot c Leftrightarrow y' = y cdot frac{1}{c} equiv y cdot c$$
Since $c$ is an arbitrary constant, any expression of it will also be a constant, so you can always "manipulate" it to be just $c$. Note that only if you have some certain restrictions for $c$, then you will need to take these in mind on how they affect the expression $1/c$.
add a comment |
up vote
7
down vote
accepted
Yes, of course. Assuming that $c in mathbb R$ is a constant, then if $c neq 0$ :
$$y = y' cdot c Leftrightarrow y' = y cdot frac{1}{c} equiv y cdot c$$
Since $c$ is an arbitrary constant, any expression of it will also be a constant, so you can always "manipulate" it to be just $c$. Note that only if you have some certain restrictions for $c$, then you will need to take these in mind on how they affect the expression $1/c$.
add a comment |
up vote
7
down vote
accepted
up vote
7
down vote
accepted
Yes, of course. Assuming that $c in mathbb R$ is a constant, then if $c neq 0$ :
$$y = y' cdot c Leftrightarrow y' = y cdot frac{1}{c} equiv y cdot c$$
Since $c$ is an arbitrary constant, any expression of it will also be a constant, so you can always "manipulate" it to be just $c$. Note that only if you have some certain restrictions for $c$, then you will need to take these in mind on how they affect the expression $1/c$.
Yes, of course. Assuming that $c in mathbb R$ is a constant, then if $c neq 0$ :
$$y = y' cdot c Leftrightarrow y' = y cdot frac{1}{c} equiv y cdot c$$
Since $c$ is an arbitrary constant, any expression of it will also be a constant, so you can always "manipulate" it to be just $c$. Note that only if you have some certain restrictions for $c$, then you will need to take these in mind on how they affect the expression $1/c$.
answered 6 hours ago
Rebellos
13.9k31243
13.9k31243
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