About this topic
Before you begin
Solve separable equations, retain initial-value domains and excluded solutions, then formulate and interpret changing-quantity models.
Learning goals
- Produce complete families, excluded solutions and initial-value solutions for polynomial-rate exponential equations
- Produce exponential solution families and initial-value solutions in the original variable after a given dependent-variable shift
- Produce quadratic-rate separable solution families, retain lost solutions and determine maximal initial-value intervals
- Return quadratic-rate solutions from a supplied dependent-variable shift and determine their maximal initial-value intervals
- Formulate, use and interpret a mathematical model
- Formulate, solve and interpret separable differential equations
Syllabus statements covered
- Include: general and particular solutions of dy/dx = f(x)g(y), including reducing to this form by a given substitution; formulating a differential equation from a problem situation; interpreting an equation and its solution contextually.
- Include: general and particular solutions of dy/dx = f(x)g(y), including reducing to this form by a given substitution; formulating a differential equation from a problem situation; interpreting an equation and its solution contextually.
In this topic
Separation, initial values and lost solutions
Retain equilibrium solutions, transform derivatives and initial-value domains, and formulate rate models with physical limits.