Differential equations

You will be able to

• Separate the variables of dy/dx = f(x)g(y), integrate both sides and write the general solution with a single constant c.
• Use an initial condition to find c before rearranging, and write the particular solution, exactly where the numbers are exact.
• State the interval on which the particular solution is valid, and explain a blow-up or an end-point where y = 0.

You will be able to

• Formulate a differential equation, with a constant of proportionality k and the correct sign, from a statement about a rate of change.
• Find k from given data, solve the equation using the initial condition, and calculate a value, a doubling time or a time to empty.
• Interpret the solution in context: t ≥ 0, the sign of k, a limiting value that is never reached, and where the model stops.