Examples of differential equations: Difference between revisions

Revision as of 15:03, 8 February 2021

Revision as of 15:10, 8 February 2021

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:<math>y = \pm e^{\left(-\int f(t)\,dt\right) + C} = \pm e^C e^{-\int f(t)\,dt}.</math>

Here, {{math|''e''^''C'' > 0}}, so {{math|±''e''<mathsup>\pm e^''C''</sup> \neq≠ 0</math>}}. But we have independently checked that {{math|1=''y'' = 0}} is also a solution of the original equation, thus

:<math>y = A e^{-\int f(t)\,dt}.</math>

with an arbitrary constant {{mvar|A}}, which covers all the cases. It is easy to confirm that this is a solution by plugging it into the original differential equation: