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Calculus Problem (Differential Equations):
Solve the first-order differential equation �′=2��y′=2xy with the initial condition �(0)=1y(0)=1. Find the solution �(�)y(x) and describe its behavior as �x varies.
Algebra Problem (Linear Algebra):
Given a 3×3 matrix �A with eigenvalues �1=4λ1=4, �2=−1λ2=−1, and �3=2λ3=2, find the corresponding eigenvectors and determine whether the matrix is diagonalizable.
Statistics Problem (Probability):
A deck of cards contains 52 cards,
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