`(dr)/(ds) = 0.75s` Find the general solution of the differential equation

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`(dr)/(ds)=0.75s`

This differential equation is separable since it has a form

  • `N(y) (dy)/dx=M(x)`

And, it can be re-written as

  • `N(y) dy = M(x) dx`

So separating the variables, the equation becomes

`dr = 0.75s ds`

Integrating both sides, it result to

`int dr = int 0.75s ds`

`r + C_1...

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`(dr)/(ds)=0.75s`

This differential equation is separable since it has a form

  • `N(y) (dy)/dx=M(x)`

And, it can be re-written as

  • `N(y) dy = M(x) dx`

So separating the variables, the equation becomes

`dr = 0.75s ds`

Integrating both sides, it result to

`int dr = int 0.75s ds`

`r + C_1 = 0.75s^2/2 + C_2`

`r+C_1 = 0.375s^2+C_2`

Isolating the r, it becomes

`r = 0.375s^2+C_2-C_1`

Since C2 and C1 are constants, it can be expressed as a single constant C.

`r = 0.375s^2 + C`

 

Therefore, the general solution of the given differential equation is `r = 0.375s^2 + C` .

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