For real $x$ consider the trivial equation

$$|y'(x)|=-e^x.$$

Since the left side is always positive and the right always negative, there is **no solution**.

Let’s try

```
DSolve(Abs(y'(x))==-Exp(x), y, x, Assumptions-> {x (Element) Reals})
```

and

```
DSolve(Sqrt(y'(x)^2)==-Exp(x), y, x, Assumptions-> {x (Element) Reals})
```

both giving the **wrong result**

```
{{y->Function({x},-E^x+Subscript((ConstantC), 1))},{y->Function({x},E^x+Subscript((ConstantC), 1))}}
```

At least

```
DSolve(RealAbs(y'(x))==-Exp(x), y, x, Assumptions-> {x (Element) Reals})
```

does return `{}`

.

Is this a bug or a feature?

*Note that this is just one example. In any case when the equation is $f(y'(x))=…$ and $f$ contains square root or absolute value the results are wrong.*