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Initial Condition(s) are a set of conditions, or a condition on the solution which will permit us to find out that solution which we are after. Initial conditions are frequently abbreviated of the form:
y(t0) = y0 and or y(k)(t0) = yk
Thus, we can say, initial conditions are values of the solution or/and its derivative(s) at exact points. As we will notice eventually, solutions to "nice sufficient" differential equations are unique and thus only one solution will meet the specified conditions.
For a specified differential equation the number of initial conditions are needed, will depend on the order of the differential equation as we will notice.
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Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon
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The complete set of all solutions is called as the solution set for the equation or inequality. There is also some formal notation for solution sets. We have to still acknowledge
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Hyperboloid of Two Sheets The equation which is given here is the equation of a hyperboloid of two sheets. - x 2 /a 2 - y 2 / b 2 + z 2 /c 2 = 1 Here is a diagram of
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