differential equation - beginner question











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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







share|cite|improve this question




























    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







    share|cite|improve this question


























      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







      share|cite|improve this question















      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






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited 6 mins ago

























      asked 6 hours ago









      gariban17

      324




      324






















          1 Answer
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          down vote



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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 $1/c$.






          share|cite|improve this answer





















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            1 Answer
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            active

            oldest

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            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 $1/c$.






            share|cite|improve this answer

























              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 $1/c$.






              share|cite|improve this answer























                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 $1/c$.






                share|cite|improve this answer












                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 $1/c$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered 6 hours ago









                Rebellos

                13.9k31243




                13.9k31243






























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