Question

Question #e964f

Answer 1

As written, the problem has no solution. See explanation for solutions to the three equations that might have been intended before the typo.

Explanation:

The problem is unsolvable as written. There is no exponent on the `3x` term.

The expression `(y+3x^)dy/dx=x` is not a proper expression for a differential equation. It is more likely that you meant to write either `(y+3x)^(dy/dx) = x`, or `(y+3x^n)dy/dx = x` (where `n` is whatever exponent you intended to include, e.g. 2, 3, etc), or possibly `(y+3x)^n dy/dx = x`

If you intended to write:

`(y+3x)^(dy/dx)=x`

Then there would indeed exist a solution, by taking `log_(y+3x)` of both sides:

`(y+3x)^(dy/dx) = x -> log_(y+3x) (y+3x)^(dy/dx)= log_(y+3x)x -> dy/dx = log_(y+3x)x`

If instead you intended to include an exponent `n`, such that the problem would be:

`(y+3x^n)dy/dx = x`

The solution would be found by dividing both sides by `(y+3x^n)`:

`(y+3x^n)dy/dx = x -> dy/dx = x/(y+3x^n)`

Where `n` is whatever exponent you intended to include.

Finally, if you intended to write:

`(y+3x)^n dy/dx = x`

You divide both sides by `(y+3x)^n` and obtain...

`(y+3x)^n dy/dx = x -> dy/dx = x/(y+3x)^n`

Where `n` is whatever exponent you intended to include.