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Differential Equations General Solutions Core 4 Maths with Liz

AIMS By the end of the lesson, you should be able to… form a first order differential equation to model real life situations solve a first order differential equation by separating the variables

What is a differential equation?

Example 1 – Writing a Differential Equation this means “is proportional to”

First order differential equations Our solution from the previous slide is considered a first-order differential equation as it involves a first-order derivative. In Core 4, you’ll be working with first-order differential equations.

You try! Write the following as differential equations. (b) (c)

continued… (d) (e)

Example 2 – Solving Differential Equations General Solutions Solve . Solution: Start by “separating the variables” by rearranging so that the L.H.S. involves only one variable, and the R.H.S. only the other. Integrate both sides. You only need to add on the constant once.

Example 2 – Solving Differential Equations General Solutions Solve .

Example 3 – Separating the Variables General Solutions Solve the following differential equation which models the population of organisms. Make P the subject. Solution: Start by separating the variables. Integrate both sides. Laws of indices! Since we’ll mainly be working with exponential growth & decay problems, we can rewrite our constant as .

You try! Show that the general solution of the differential equation is Solution:

Example 4 – Separating the Variables General Solutions Find a general solution for the following differential equation. Make y the subject. Solution: Start by separating the variables. Integrate both sides.

Challenge Question! Find a general solution for the differential equation. Solution:

Independent Study Mymaths – Differential Equations Optional practise: Core 4 textbook, Pg. 72, Exercise C DUE NEXT LESSON