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Certainly! Here's an advanced math question involving calculus and differential equations:

$**$Question:$**$

Consider the differential equation $(\frac{dy}{dx}=y^2-x^2).$

Find the particular solution of the differential equation given that $(y(1)=2).$

Determine the intervals of increase and decrease for the solution.

Calculate the second derivative and discuss the concavity of the curve for the solution.

Sketch the graph of the solution in the range $(x=-2)(x=2),$ indicating the key features

based on your analysis.

This question combines several aspects of advanced mathematics, including solving differential

equations, analyzing the behavior of the solution, and applying calculus concepts like concavity

and curve sketching.