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
    2 days ago






  • 1




    This is a known form !
    – Yves Daoust
    2 days ago















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




















  • 1




    $dfrac{z}{2+z} dz=dt$
    – Nosrati
    2 days ago






  • 1




    This is a known form !
    – Yves Daoust
    2 days ago













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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edited 2 days ago

























asked 2 days ago









galah92

25218




25218








  • 1




    $dfrac{z}{2+z} dz=dt$
    – Nosrati
    2 days ago






  • 1




    This is a known form !
    – Yves Daoust
    2 days ago














  • 1




    $dfrac{z}{2+z} dz=dt$
    – Nosrati
    2 days ago






  • 1




    This is a known form !
    – Yves Daoust
    2 days ago








1




1




$dfrac{z}{2+z} dz=dt$
– Nosrati
2 days ago




$dfrac{z}{2+z} dz=dt$
– Nosrati
2 days ago




1




1




This is a known form !
– Yves Daoust
2 days ago




This is a known form !
– Yves Daoust
2 days ago










1 Answer
1






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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
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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























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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 2 days ago









        Mohammad Riazi-Kermani

        40.2k41958




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