Differential Equations (Integration 3) - [Pure 4]. Flashcards
1
Q
What does the derivative of dy/dx represent?
A
The rate of change of y with respect to x.
2
Q
What does the derivative of dy/dt represent?
A
The rate of change of y with respect to time.
(More common in these sorts of questions).
3
Q
If ‘a’ is proportional to ‘b’, what can we write?
A
- a ∝ b.
- Or a = kb, where ‘k’ is the constant of proportionality.
4
Q
What do you need to use to solve differential equations?
A
Integration.
5
Q
What is the difference between a General Solution and a Particular Solution?
A
- A General Solution contains a ‘+c’ term after the integration which has no bounds.
- A Particular Solution has no unknown constants as there are bounds to the integration which can be subbed in.
6
Q
When using Differential Equations, what does ‘y’ differentiate to?
A
(1/y)(dy/dx).
7
Q
How do you get dx/dy?
A
1/(dy/dx).
8
Q
How do you get dy/dx from dy/dt and dt/dx for example?
A
dy/dx = dy/dt x dt/dx.
9
Q
What is the **rate of change of volume ** equal to?
A
dV/dt.
10
Q
What is the **rate of change of depth ** equal to?
A
dh/dt.
