## Differential equations

Differential equations provide calculations where things happen with a changing rate. The rate that things change may depend on another value which is changing too.

For example, compound interest or rabbit populations both get bigger and bigger. Moreover, they get bigger faster! as time goes along. Their rate of change increases as time increases. Differential equations have application in STEM as well as economics.

• DE1 First order separable

What is a first order separable differential equation? A first order variables separable differential equation is one in which the variables (represented by pronumerals or letters) can be separated into either side of the equation (i.e. the = sign).

• DE2 First order linear

What is a first order linear unseparable differential equation? If a differential equation is unseparable, this means the variables (represented by pronumerals or letters) cannot be isolated. That means you cannot reorganise the formula so that the wanted variable is on one side of the equation alone. You will need to resort to other numerical or analytical methods to solve these differential equations. Read this sheet to find out how.

• DE3 Second order homogeneous

What is a second order homogenous differential equation? A second order homogenous differential equation is an expression that includes a function of a variable (say y), its derivative (y’) and a second derivative (y’’) and this expression is equal to zero. Read this sheet to find out how to solve these.

• DE4 Second order non-homogeneous

What is a second order non-homogenous differential equation? A second order non homogenous DE is an expression that includes a function of a variable (say y), its derivative (y’) and a second derivative (y’’), but this time the expression is NOT equal to zero. Read this sheet to find out how to solve these.

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