The given problem appears to involve several mathematical expressions that need careful interpretation. Let's break them down step by step.

First Equation:

You presented:

$y = \text{se abc}(x) + \frac{\tan(xs)}{s} \cdot i \cdot 2 \cdot \frac{dy}{dx} = 1 + y^2$

Interpretation:

1. se abc(x): This term is not a standard mathematical function. Perhaps it refers to a typo or a special function. If it's "sec(x)" (the secant function), it would make more sense. So, this might be $\sec(x)$.

2. $\frac{\tan(xs)}{s} \cdot i \cdot 2 \cdot \frac{dy}{dx}$: This term involves a product of tangent function, a constant $s$, imaginary unit $i$, and the derivative $\frac{dy}{dx}$. It seems to be a complex expression depending on $x$ and $s$.

3. $1 + y^2$: This is a standard form for the Riccati differential equation.

Given this, your first equation might be related to a Riccati-type differential equation involving complex terms.

Second Equation:

$x = \frac{\cos(\theta) - \sin(\theta)}{\cos(\theta) + \sin(\theta)} \cdot s \cdot \cot\left(\frac{d}{d\theta}(x)\right) + x^2 + 1 = 0$

Interpretation:

1. $\frac{\cos(\theta) - \sin(\theta)}{\cos(\theta) + \sin(\theta)}$: This part looks like a trigonometric simplification. The ratio between sine and cosine is generally linked to tangent functions, so this might be simplified further.

2. $s \cdot \cot\left(\frac{d}{d\theta}(x)\right)$: Here, $s$ is multiplied by the cotangent of the derivative of $x$ with respect to $\theta$. It appears to be a higher-order differential equation with respect to $x$ and $\theta$.

3. $x^2 + 1 = 0$: This implies $x$ is purely imaginary because the solution to $x^2 + 1 = 0$ is $x = i$ or $x = -i$.

Summary of Equations:

1. The first equation seems to be a complex differential equation, potentially Riccati-type, depending on an unknown function $\text{se abc}(x)$.
2. The second equation involves a complex trigonometric-differential form with $x$ likely being a function of $\theta$ and satisfying a purely imaginary condition.

Next Steps:

To clarify these equations further:

1. Can you confirm whether "se abc(x)" is supposed to be "sec(x)" or another function?
2. Do the variables $s$, $i$, and $\theta$ have specific meanings in the context of the problem?

Relative Questions:

1. Could "se abc(x)" be a known function, or is it a typo for secant?
2. How do the variables $s$ and $i$ relate to the problem? Are they constants?
3. Is $x$ meant to be purely imaginary based on the equation $x^2 + 1 = 0$?
4. Would you like to simplify the trigonometric parts of the second equation?
5. How does the complex term $i \cdot \frac{dy}{dx}$ impact the solution of the first equation?

Tip:

When dealing with complex functions and differential equations, it's crucial to clarify all terms and symbols to avoid confusion during the solution process.