Differential Equations: Separation of Variables & Singular Solutions скачать в хорошем качестве

Differential Equations: Separation of Variables & Singular Solutions

#DifferentialEquations #Calculus #Manim #Math #Python #Equations #mathematics #Separation #Variables #Singular #Integration #integrationformula In this video, we solve a differential equation using the Separation of Variables method. We explore both the algebraic solution and the geometric interpretation. A key focus of this example is identifying the "Lost Solution" (Singular Solution) that is often missed when dividing by variables. The Equation: √(y² + 1) dx = xy dy Timecodes: 0:00 - The Equation 0:25 - Separation of Variables 0:55 - Integration & Substitution 1:40 - General Solution 2:00 - The Lost (Singular) Solution 2:35 - Geometric Visualization (Vector Field)    • Theorem: Every Convergent Sequence is Boun...      • Solving Differential Equation xy\,dx + (x+...      • Does it Converge or Diverge? Integral of 1...      • Integral of 1/x^2: Power Rule with Negativ...      • Complex Analysis: Finding the Laurent Seri...      • Metric Spaces: Definition, Axioms, and Exa...