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Initial horizontal speed of particle = 10cos(p) m/s. Initial vertical speed of particle = 10sin(p) m/s. ('U' in suvat.) There are no forces other than gravity acting on the particle so the vertical accele...

To use the integrating factor method your first order DE must be of the form dy/dx + f(x)y =g(x), where f(x) and g(x) are any functions that depend only on x. lets say f(x)=3x^2 and g(x)=2, (If I feel the...

There are as many fractions as there are factors of the denomenator.  If the denomenator of one of the partial fractions is linear then the numerator is a constant. If the denomenator is a linear term squ...

If you have a claim which says something about every element in a list of elements with each element depending on previous elements, induction might be a useful starting point. In your exams, that "l...

dy/dx = (dy/du)(1/x), d^2(y)/dx^2 = (d^2(y)/du^2)(1/(x^2)) - (dy/du)*(1/(x^2))   

(x^2)( (d^2(y)/du^2)(1/(x^2)) - (dy/du)(1/(x^2)) ) + x(dy/du)*(1/x) + y = 0