What does it mean for a function to be a solution of a differential equation? I think I understand, but I still don't have a simple or intuitive understanding.
What does it mean for a function to be a solution of a differential equation?
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1What does it mean for a number to be a solution of an equation? – 2011-12-09
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0A number is a solution when it fits within the range of answers that the function generates. For differential equations an equation is a solution when the equation is created satisfies the derivative's range. – 2011-12-09
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2Not quite. An equation is a statement about numbers involving an unknown. A number solves an equation if, when substituted for the unknown, it makes the statement true. Likewise, a differential equation is a statement about functions involving an unknown function. A function solves a differential equation if, when substituted, the statement is true. – 2011-12-09
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0Simple? If you "plug in" the function to the differential equation and it gives an equality, then it's a solution! – 2011-12-14