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How to Separate Equation Transcript

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Multiply both sides by DX:Dy = (1/y) DX. Multiply both sides by y: y Dy = DX. Put the integral sign in front: y Dy = DX. Integrate each side: (y2)/2 = x + C. Multiply both sides by 2: y2 = 2(x + C)
The method for solving separable equations can therefore be summarized as follows: Separate the variables and integrate. Example 1: Solve the equation 2 y Dy = (x 2 + 1) DX. Example 4: Find all solutions of the differential equation (x 2 1) y 3 DX + x 2 Dy = 0.
0:06 10:27 Suggested clip Differential Equations: Separation of Variables — YouTubeYouTubeStart of suggested client of suggested clip Differential Equations: Separation of Variables — YouTube
Note that in order for a differential equation to be separable all the y's in the differential equation must be multiplied by the derivative and all the x's in the differential equation must be on the other side of the equal sign.
A first-order differential equation is said to be separable if, after solving it for the derivative, Dy DX = F(x, y), the right-hand side can then be factored as a formula of just x times a formula of just y, F(x, y) = f (x)g(y).
0:03 7:33 Suggested clip Differential Equation l Nonlinear Differential Equation l Solution of ... YouTubeStart of suggested client of suggested clip Differential Equation l Nonlinear Differential Equation l Solution of ...
In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.
Separation of Variables. Separation of variables is a method of solving ordinary and partial differential equations. ... breaking the resulting equation into a set of independent ordinary differential equations, solving these for,, ..., and then plugging them back into the original equation.
Multiply both sides by DX:Dy = (1/y) DX. Multiply both sides by y: y Dy = DX. Put the integral sign in front: y Dy = DX. Integrate each side: (y2)/2 = x + C. Multiply both sides by 2: y2 = 2(x + C)
The method of separation of variables is also used to solve a wide range of linear partial differential equations with boundary and initial conditions, such as the heat equation, wave equation, Laplace equation, Helmholtz equation and bi harmonic equation.
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