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SingaporeFurther Maths

Differential Equations

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we solve first-order differential equations by separating variables and by the integrating factor method?

Solve first-order differential equations by separation of variables and by the integrating factor method, applying initial conditions
A focused answer to the H2 Further Mathematics outcome on first-order differential equations. Separation of variables, the integrating factor method for linear equations, general and particular solutions, and applying initial conditions.
11 min answer →

How do we set up a differential equation to model a real situation and interpret its solution?

Formulate differential equations from descriptions of rates of change and interpret the solutions in context, including long-term behaviour
A focused answer to the H2 Further Mathematics outcome on modelling with differential equations. Translating a rate description into an equation, solving the resulting first- or second-order model, interpreting constants, and analysing long-term behaviour and limiting values.
11 min answer →

How do we solve a non-homogeneous second-order linear differential equation using a complementary function and a particular integral?

Solve non-homogeneous second-order linear differential equations by finding the complementary function and a particular integral for standard forcing terms
A focused answer to the H2 Further Mathematics outcome on non-homogeneous second-order ODEs. The complementary function plus particular integral structure, trial forms for polynomial, exponential and trigonometric forcing, the breakdown case, and fitting initial conditions last.
12 min answer →

How do we solve a homogeneous second-order linear differential equation with constant coefficients using the auxiliary equation?

Solve homogeneous second-order linear differential equations with constant coefficients using the auxiliary equation, covering real, repeated and complex roots
A focused answer to the H2 Further Mathematics outcome on homogeneous second-order linear ODEs. The auxiliary equation, the three cases of distinct real, repeated and complex roots, and applying two initial conditions to fix the constants.
11 min answer →

How do we solve a coupled system of first-order linear differential equations by reducing it to a single second-order equation?

Solve coupled systems of first-order linear differential equations by reduction to a single second-order equation
A focused answer to the H2 Further Mathematics outcome on coupled linear systems. Eliminating one variable to obtain a single second-order equation, solving it, recovering the second variable, and applying initial conditions to both.
11 min answer →