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Ordinary Differential Equations of First Order

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Video-01

This video explains that Ordinary Differential Equations model real-world change, such as population growth, using functions of a single variable. It teaches how to identify the order (highest derivative) and degree (the power of that derivative). The lesson includes step-by-step examples on simplifying equations to find these values correctly.

Video-02

This video explains how to identify and solve Exact Differential Equations of the form Mdx + Ndy = 0. It teaches the "test for exactness" by checking if ∂M/∂y = ∂N/∂x and provides the integration formula for the general solution. The lesson includes five step-by-step examples ranging from linear and trigonometric functions to more complex exponential terms

Video-03

This video explains how to solve Non-Exact Homogeneous Differential Equations by converting them into exact ones using an Integrating Factor (I.F. = 1/(Mx + Ny)). It demonstrates the process of verifying homogeneity, calculating the I.F., and multiplying it through the original equation to make it integrable. The tutorial covers three detailed examples with varying degrees and concludes with practice problems to reinforce the method.

Video-04

This video explains solving Type-2 Non-Exact Equations of the form yf(xy)dx + xg(xy)dy = 0. It uses the Integrating Factor I.F. = 1/(Mx - Ny) to transform them into exact equations. Detailed examples show how to apply this formula to trigonometric and multi-variable problems.

Video-05

This video explains how to solve Type-3 Non-Exact Differential Equations where the equation can be made exact using an Integrating Factor that depends only on x. It teaches how to verify if an equation fits this type by checking conditions and demonstrates calculating the Integrating Factor e^(∫f(x)dx) with examples.

Video-06

This video explains solving Type-4 Non-Exact Equations where the integrating factor depends only on y. It uses the formula I.F. = e^(∫g(y)dy) to transform non-exact equations into exact ones for integration. The lesson includes practical examples and practice problems.

Video-07

This video explains the standard form dy/dx + Py = Q and the method for solving First-Order Linear Differential Equations using the Integrating Factor (I.F. = e^(∫P dx)). Includes multiple examples.

Video-08

This video explains Bernoulli’s Equation and its transformation into a linear differential equation using substitution methods, followed by solving using an integrating factor.

Video-09

This video defines Orthogonal Trajectories as curves intersecting at 90° angles and explains the solving procedure with differentiation, slope replacement, and integration.