# Tag Archives: Equation

## Population Differential Equations and Laplace Transform

Malthus Model : Total population : Birth-rate per capita : Death-rate per capita Solution to D.E.: where . Logistic Equation Logistic Case 1: Increasing population () The second expression can be derived from the first: divide by in both the … Continue reading

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## Linear First Order ODE, Bernoulli Equations and Applications

Linear First Order ODE DE of the form: . Integrating factor: . (Remember to have a constant when integrating the numerator .) Integration by parts Acronym: LIATE (Log, Inverse Trig., Algebraic, Trig., Exponential), where L is the best choice for … Continue reading

## Trigonometric Identities and Differential Equations

Trigonometric Identities Reduction to Separable Form Equations of the form Set . Then and . Thus the original equation becomes which is separable. Linear Change of Variable can be solved by setting . Newton’s Law of Cooling Rate of change … Continue reading