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Separable Equation

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- 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

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Example 3

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- 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.

SOLUTION