UCL Online STEP and AEA Preparation Sessions
Session 15: Differential equations
Differential equations describe how mathematical systems change. There are a
variety of techniques for solving differential equations and examples of these will be
given in this session.
A question type at this level involves being given a differential equation which is not
immediately solvable using standard techniques. Typically a substitution is made
which results in a differential equation which can be solved.
When making substitutions in differential equations care is needed to keep track of
the relationships between variables, which variable differentiation is with respect to
and using implicit differentiation accurately.
Sometimes problems will require a real life situation to be modelled by appropriate
differential equations.
Being able to interpret the solution of a differential equation is also very important
Sketching solutions to differential equations will be considered
Example problem
2
dy
 dy 
Find two solutions of the differential equation 3    2 x  1
dx
 dx 