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Solve the differential equations dx/dt=2x+y+1 and dy/dt=4x-y+1 given that when t=0 x=20 and y=60. (A2 Further pure)

These questions are really mean but if given in the exam give ALOT of marks and whilst scary at first follow a very general pattern. First I would take either equation and re-arrange for the lone variable...

Answered by • Further Mathematics tutor

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What is the equation of a circle with centre (3,4) and radius 4?

The general equation of a circle is (x-a)^2 + (y-b)^2 = r^2 where the centre is (a,b) and radius r.
Therefore the equation of this circle is (x-3)^2 +(y-4)^2 = 4^2 ...or 16
Sometimes its easie...

Answered by Isobel L. • Further Mathematics tutor

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Integrate tan(x) wrt x

Use substitutionlet u = cos(x)du = - sin(x)dxint(tan(x)) dx = int(sinx/cosx) dx = - int(1/u) du = - ln(u) + c= ln(secx) + c

Answered by Mathew H. • Further Mathematics tutor

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Find a vector that is normal to lines L1 and L2 and passes through their common point of intersection where L1 is the line r = (3,1,1) + u(1,-2,-1) and L2 is the line r = (0,-2,3) + v(-5,1,4) where u and v are scalar values.

We will use the cross product of these two vectors to help us find the perpendicular vector. The cross product works by finding a vector which has no effect on the position of a point with respect the the...

Answered by Aengus R. • Further Mathematics tutor

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Find the general solution of the differential equation d^2y/dx^2 - 2(dy/dx) = 26sin(3x)

2 Parts to this question - requires a complimentary function (treating equation as if right-hand side (RHS) = 0) and a particular integral (the general solution for where the RHS = 26sin(3x) )
1) The...

Answered by Matt P. • Further Mathematics tutor

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