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# Differential Equations (Metric)

## Class Details

**Tom
Baker**

Learn, or revise, solving first order differential equations by various methods, solving second order differential equations with constant coefficients, and classifying the critical points of systems.

## Units

### First Order

Solving differential equations of the form \(dy/dx=f(x,\,y)\). Part of this topic is found on A-level courses, and the rest is Further Maths.

Solving differential equations of the form \(dy/dx = f(x)\,g(y)\), by separating the variables.

Solving differential equations that can be written in the form \(d/dx(f(x,\,y))=0\).

### Second Order

Solving differential equations of the form \(a\,d^2y/dx^2+b\,dy/dx+c\,y=f(x)\). This is a Further Maths topic; courses that require Further Maths may assume it.

Solving differential equations of the form \(a\,d^2y/dx^2+b\,dy/dx+c\,y=0\); oscillatory and exponential solutions.

Solving differential equations of the form \(a\,d^2y/dx^2+b\,dy/dx+c\,y=f(x)\) using a complementary function and a particular integral.

Strong, critical and weak damping; resonance.

### Qualitative Methods

Classifying the critical points of systems of the form \(dx/dt = f_1(x,\,y)\), \(dy/dt = f_2(x,\,y)\). This is part of the First Year content of some Science and Engineering courses at Imperial.