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Differential Equations (Metric)
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.
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 \(d/dx(f(x,\,y))=0\).
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.
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.