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Proving the Schwarz inequality |⟨𝛼|𝛽⟩|² ≤ ⟨𝛼|𝛼⟩⟨𝛽|𝛽⟩ (Quantum Mechanics)

Application of Differential Equations - Decay and Decomposition

Application of Differential Equations - Population Growth

Orthogonal Trajectories

Coefficients Linear in the Two Variables (x + y - 2)dx - (x -4y -2)dy = 0

Substitution Suggested by the Equation (3tanx - 2cosy)sec²xdx + tanxsinydy = 0

Bernoulli Type 2xyy' = y² - 2x³; y(1) = 2

Substitution Suggested by the Equation [1 + (x + y)²]dx + [1 + x(x + y)]dy = 0

Bernoulli Type 2ydx + (x³lny - x)dy = 0

Linear Equation of Order One (2ycosx + sin⁴x)dx - sinxdy = 0; when x=(𝝅/2), y=1

Exact Equation (sint - 3s² + 5)ds + (t + scost)dt = 0

Exact Equation (2uv³ - 3v)du + (3u²v² - 3u + 4v)dv = 0