If you dont have time for all of it, thats ok, just skip the hardest part, I need at least 70% correct.1)Calculate the integrals.a)∫(cos x / 1 + (sin^2 )*x)*dxb)∫(x^2/(x^2)-1))dx2)a) solve the difference equation yn + yn−1 – 12yn−2 = 100n.b)
Find the general solution to the differential equation y^n- 6y’ + 13y = 0.c) Solve the initial value problem y^n- 6y’ + 13y = 0, y(0) = 0, y’(0) = 10.d) Solve the differential equation y’ – 4x√y = 0.3)The curve 3x^2 – 2xy + y^2 = 9 is an ellipse. According to Kepplers laws the planets move in such elliptical orbits.a) Show that the point (2, 3) is on the curve, and find the equation for the tangent in this point.b) Assume that the curve is the orbit of a particle.
When the particle is in the point (2,3), it`s got the speed 2m/s in the x-direction. Find the speed of the particle in the y-direction.4)Wich point on the curve y = (4/√x) is closest to center (origo), and what is the distance from center (origo) to this point on the curve?”
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