ODE and linear substitution











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I'm having a hard time solving the following differential equation:
$$dot{x}=frac{1}{t+2x}$$



I tried introducing $z = t+2x$, and so $dot{z}=1+2dot{x}$, and I got the following:
$$dot{z}=frac{2}{z}+1$$
Which is also not in a known form. What am I missing?






differential-equations







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  • 1




    $dfrac{z}{2+z} dz=dt$
    – Nosrati
    Nov 21 at 13:28






  • 1




    This is a known form !
    – Yves Daoust
    Nov 21 at 13:39















up vote
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favorite












I'm having a hard time solving the following differential equation:
$$dot{x}=frac{1}{t+2x}$$



I tried introducing $z = t+2x$, and so $dot{z}=1+2dot{x}$, and I got the following:
$$dot{z}=frac{2}{z}+1$$
Which is also not in a known form. What am I missing?






differential-equations







share|cite|improve this question




















  • 1




    $dfrac{z}{2+z} dz=dt$
    – Nosrati
    Nov 21 at 13:28






  • 1




    This is a known form !
    – Yves Daoust
    Nov 21 at 13:39













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I'm having a hard time solving the following differential equation:
$$dot{x}=frac{1}{t+2x}$$



I tried introducing $z = t+2x$, and so $dot{z}=1+2dot{x}$, and I got the following:
$$dot{z}=frac{2}{z}+1$$
Which is also not in a known form. What am I missing?






differential-equations







share|cite|improve this question















I'm having a hard time solving the following differential equation:
$$dot{x}=frac{1}{t+2x}$$



I tried introducing $z = t+2x$, and so $dot{z}=1+2dot{x}$, and I got the following:
$$dot{z}=frac{2}{z}+1$$
Which is also not in a known form. What am I missing?






differential-equations




differential-equations






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share|cite|improve this question













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edited Nov 21 at 13:27

























asked Nov 21 at 13:21









galah92

25418




25418








  • 1




    $dfrac{z}{2+z} dz=dt$
    – Nosrati
    Nov 21 at 13:28






  • 1




    This is a known form !
    – Yves Daoust
    Nov 21 at 13:39














  • 1




    $dfrac{z}{2+z} dz=dt$
    – Nosrati
    Nov 21 at 13:28






  • 1




    This is a known form !
    – Yves Daoust
    Nov 21 at 13:39








1




1




$dfrac{z}{2+z} dz=dt$
– Nosrati
Nov 21 at 13:28




$dfrac{z}{2+z} dz=dt$
– Nosrati
Nov 21 at 13:28




1




1




This is a known form !
– Yves Daoust
Nov 21 at 13:39




This is a known form !
– Yves Daoust
Nov 21 at 13:39










1 Answer
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You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$



$$ int frac {zdz}{z+2}=int dt$$






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    You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$



    $$ int frac {zdz}{z+2}=int dt$$






    share|cite|improve this answer

























      up vote
      0
      down vote













      You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$



      $$ int frac {zdz}{z+2}=int dt$$






      share|cite|improve this answer























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        up vote
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        You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$



        $$ int frac {zdz}{z+2}=int dt$$






        share|cite|improve this answer












        You have a separable differential equation $$ dot {z}=frac {z+2}{z}$$



        $$ int frac {zdz}{z+2}=int dt$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 21 at 14:12









        Mohammad Riazi-Kermani

        40.3k41958




        40.3k41958






























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