It seems like the expression you provided is a bit unclear, likely due to some formatting issues. I'll attempt to interpret it in a mathematically consistent way. Based on what you've written, I think you might be aiming for something like the following:

$\frac{dy}{dx} = e^{x + y} + x^2 e^{x^2 + y}$

This is a first-order nonlinear differential equation. Let me know if this interpretation is correct or if you'd like me to adjust it.

Solving the Equation

1. The equation can’t be separated easily, and no direct simplifications apply, so advanced techniques like numerical approximation or exact methods are needed.
2. To proceed, one could use implicit differentiation, numerical methods, or attempt a solution via series expansion if the context of the problem is provided.

Would you like me to walk you through any specific method or steps for solving this?

Related Questions:

1. How can you solve a first-order nonlinear differential equation like this one?
2. What are numerical methods for solving differential equations (like Runge-Kutta)?
3. How does one approach implicit differentiation with nonlinear terms?
4. What is the significance of the exponential function in differential equations?
5. Are there any specific boundary conditions for this problem?

Tip:

When dealing with nonlinear differential equations, look for patterns or specific forms (like Bernoulli's or Riccati equations) that could simplify the process of finding solutions.