1. Please hand in your assignment at the front desk as you come in 

2. Differential Equations General Solutions
Core 4 Maths with Liz

3. 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

4. What is a differential equation?

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

6. 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.

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

8. continued…
(d)
(e)

9. 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.

10. Example 2 – Solving Differential Equations General Solutions
Solve

11. 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

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

13. 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.

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

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