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Line 13: − To find <math>y/,</math>, manipulate the substitutions of M and N to get <math>M \partial t = \partial \phi</math> and <math>N \partial y = \partial \phi</math>. Integrate both sides. To get the main function φ write the sum of each term found in each equation. For terms that appear in both equations, only write them once. − + + + +
Exact differential equation (view source)
Revision as of 18:55, August 2, 2010
, 18:55, August 2, 2010no edit summary
To find the solution of this equation, we assume that the solution is φ = constant. We assume that <math>\frac{\partial \phi}{\partial t} = M</math> and <math>\frac{\partial \phi}{\partial y} = N</math>. (If we substitute M and N back into (1), it yields <math>(\frac{\partial \phi}{\partial t}) dt + (\frac{\partial \phi}{\partial y}) dy = 0</math>, which makes sense.)
To find the solution of this equation, we assume that the solution is φ = constant. We assume that <math>\frac{\partial \phi}{\partial t} = M</math> and <math>\frac{\partial \phi}{\partial y} = N</math>. (If we substitute M and N back into (1), it yields <math>(\frac{\partial \phi}{\partial t}) dt + (\frac{\partial \phi}{\partial y}) dy = 0</math>, which makes sense.)
To solve the expression for <math>y/,</math>, use the quadratic formula.
To find <math>y</math>, manipulate the substitutions of M and N to get <math>M \partial t = \partial \phi</math> and <math>N \partial y = \partial \phi</math>. Integrate both sides. To get the main function φ write the sum of each term found in each equation. For terms that appear in both equations, only write them once.
To solve the expression for <math>y</math>, use the quadratic formula.
[[Category:Calculus]]
[[Category:Calculus]]
[[Category:Differential Equations]]
[[Category:Differential Equations]]