High School Can an Impossible Differential Be Solved in Calculus?

[cdamberg21]

Hey, someone I know told me that the differential dy/dx= 24x/(2x+3) is not possible to solve... Is this true? If not what's the differential for it. This is my first year of calc in high school so my apologies if I butchered some of the terminology.

 

[BvU]

hey cdamberg, $\qquad$ $\qquad$ !

Here at PF we post this kind of stuff in a homework forum
and we post an attempt at solution (otherwise helpers are not allowed to assist!)

This is my first year of calc in high school

Good ! So you know how to solve differential equations already ? Which ones ?

 

[fresh_42]

I moved it to "Calculus" since it is more of a general question than actual homework.

... and welcome @cdamberg21 to PF. @BvU is right, we have quite a few homework forums for all kind of help in your daily questions around exercises. You're welcome to post there, if you have trouble with certain questions: the distinction is roughly: has it numbers, then it's homework, is it a general question, then it normally belongs to the technical forums.

 

[mathman]

You don't need to solve a differential equation. Just integrate the right side.

 

[cdamberg21]

hey cdamberg, $\qquad$ $\qquad$ !

Here at PF we post this kind of stuff in a homework forum
and we post an attempt at solution (otherwise helpers are not allowed to assist!)
Good ! So you know how to solve differential equations already ? Which ones ?

Just learned to solve via separation of variables, wrapping up the end of the AP Calc AB curriculum soon.

 

[BvU]

If you can write $12\ {2x\over 2x+3} \$ in a form like $\ a + {b\over 2x+3}\$ then you have two terms that you know how to integrate

 

[cdamberg21]

I moved it to "Calculus" since it is more of a general question than actual homework.

... and welcome @cdamberg21 to PF. @BvU is right, we have quite a few homework forums for all kind of help in your daily questions around exercises. You're welcome to post there, if you have trouble with certain questions: the distinction is roughly: has it numbers, then it's homework, is it a general question, then it normally belongs to the technical forums.

Ok thanks, it is meant to be more of a general question as to how to solve an integral in the form of kx / (ax+b)

 

[BvU]

Still belongs in homework.
Can you folow the path indicated in #6 ?

 

[aheight]

Hey, someone I know told me that the differential dy/dx= 24x/(2x+3) is not possible to solve... Is this true? If not what's the differential for it. This is my first year of calc in high school so my apologies if I butchered some of the terminology.

I would not expect you to solve a differential equation in your first year of Calculus. It's important however to get the terminology precise: The expression $\frac{dy}{dx}=\frac{24x}{2x+3}$ is just the expression for the derivative of y with respect to x. And that derivative it the expression on the right side. So as written, you have already solved for the derivative of y. Now, if y is not known, then you can integrate both sides if the expression to determine y. I do not recall however when integration is studied in the first year of Calculus so you may not yet have gotten to that point. And differentials are terms like dy and dx.

 

[BvU]

Ok thanks, it is meant to be more of a general question as to how to solve an integral in the form of kx / (ax+b)

The method is called partial fractions decomposition (which google).$${kx\over ax+b} = {k\over a}{ax\over ax+b} = {k\over a}\left ( {ax+b\over ax+b} - {b\over ax+b} \right ) = {k\over a}\left ( 1 - {b\over ax+b} \right ) $$ and you know the primitives of these two terms.