How to solve analytically this equation?

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I need to solve the next equation and to find $x_1$:



$$dfracd(x_0x_1)dz=-8dfracdx_0dzdfrac1r-z(r-1)$$



where $x_0$, $x_1$, $z$ are variables, and $r$, $beta$ are constants.



At this point is it possible to multiply whole equation with $dz$, will I lose some information because of the therm $dfrac1r-z(r-1)$?



On the other side, I have expression for $x_0=f(z)$, it is dependent on $z$:



$x_0=left(1+dfracbetar-1left( 1-dfrac1(r-z(r-1))^3 right)right)^0.5$



On which side I need to go to integrate this equation?







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  • You posted the same question on MO. I think that crossposting, without mentioning it, is considered a bad practice, see Moderator Supported (Official) Guidelines for “Legitimate” CrossPosting?.
    – user539887
    Aug 22 at 9:28














up vote
0
down vote

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I need to solve the next equation and to find $x_1$:



$$dfracd(x_0x_1)dz=-8dfracdx_0dzdfrac1r-z(r-1)$$



where $x_0$, $x_1$, $z$ are variables, and $r$, $beta$ are constants.



At this point is it possible to multiply whole equation with $dz$, will I lose some information because of the therm $dfrac1r-z(r-1)$?



On the other side, I have expression for $x_0=f(z)$, it is dependent on $z$:



$x_0=left(1+dfracbetar-1left( 1-dfrac1(r-z(r-1))^3 right)right)^0.5$



On which side I need to go to integrate this equation?







share|cite|improve this question






















  • You posted the same question on MO. I think that crossposting, without mentioning it, is considered a bad practice, see Moderator Supported (Official) Guidelines for “Legitimate” CrossPosting?.
    – user539887
    Aug 22 at 9:28












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I need to solve the next equation and to find $x_1$:



$$dfracd(x_0x_1)dz=-8dfracdx_0dzdfrac1r-z(r-1)$$



where $x_0$, $x_1$, $z$ are variables, and $r$, $beta$ are constants.



At this point is it possible to multiply whole equation with $dz$, will I lose some information because of the therm $dfrac1r-z(r-1)$?



On the other side, I have expression for $x_0=f(z)$, it is dependent on $z$:



$x_0=left(1+dfracbetar-1left( 1-dfrac1(r-z(r-1))^3 right)right)^0.5$



On which side I need to go to integrate this equation?







share|cite|improve this question














I need to solve the next equation and to find $x_1$:



$$dfracd(x_0x_1)dz=-8dfracdx_0dzdfrac1r-z(r-1)$$



where $x_0$, $x_1$, $z$ are variables, and $r$, $beta$ are constants.



At this point is it possible to multiply whole equation with $dz$, will I lose some information because of the therm $dfrac1r-z(r-1)$?



On the other side, I have expression for $x_0=f(z)$, it is dependent on $z$:



$x_0=left(1+dfracbetar-1left( 1-dfrac1(r-z(r-1))^3 right)right)^0.5$



On which side I need to go to integrate this equation?









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 21 at 20:43

























asked Aug 21 at 13:19









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  • You posted the same question on MO. I think that crossposting, without mentioning it, is considered a bad practice, see Moderator Supported (Official) Guidelines for “Legitimate” CrossPosting?.
    – user539887
    Aug 22 at 9:28
















  • You posted the same question on MO. I think that crossposting, without mentioning it, is considered a bad practice, see Moderator Supported (Official) Guidelines for “Legitimate” CrossPosting?.
    – user539887
    Aug 22 at 9:28















You posted the same question on MO. I think that crossposting, without mentioning it, is considered a bad practice, see Moderator Supported (Official) Guidelines for “Legitimate” CrossPosting?.
– user539887
Aug 22 at 9:28




You posted the same question on MO. I think that crossposting, without mentioning it, is considered a bad practice, see Moderator Supported (Official) Guidelines for “Legitimate” CrossPosting?.
– user539887
Aug 22 at 9:28















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