Separable Equation

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# Separable Equation - PowerPoint PPT Presentation

Separable Equation. Step 1 – identify the problem as a separable equation Step 2 – Separate the equation into the form. Rearrange to Step 3 – integrate both sides of the equation , adding one arbitrary constant, say C, to the x side. Evaluate

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## PowerPoint Slideshow about ' Separable Equation' - nassor

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Presentation Transcript
Separable Equation
• Step 1 – identify the problem as a separable equation
• Step 2 – Separate the equation into the form. Rearrange to
• Step 3 – integrate both sides of the equation, adding one arbitrary constant, say C, to the x side. Evaluate
• Step 4 - If there is an initial condition, then substitute it to obtain the value of C
Example 1

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Example 2

SOLUTION

Example 3

SOLUTION

HOMOGENEOUS Equation
• Step 1- Write to the general form . Make sure this equation is homogeneous. Need to show
• Step 2 - Use substitution and into homogeneous equation in Step 1.
• Step 3 - Separate the variables x and v in the resulting equation.
• Step 4 - Integrate both sides of the equation and then put only a constant, say C on the right integration. When this equation is integrated then we obtain a relationship between x and v.
• Step 5 - Then by substituting we have the required solution.
• Step 6 - If there is an initial condition, and then use it to obtain the value for C.
Example 2

SOLUTION