Express the equation x²-x+ y²+z² = 1 in cylindrical coordinates. 2 z² = 1-rcos0+ r² Oz² = 1+rcos 0-12 Z Oz²=1+ cos 0-12 z² = 1+rsin 0-12

Find the point on the y-axis which is equidistant from (2,5,-3) and (-3,6,1). After getting the value of y, convert the coordinates to cylindrical coordinates assuming in the new coordinates, the value of x=1, z=1

Express a general solution to 2x (1 — х)у" + (3 — 10х)у — бу %3D 0 Using Gaussian hypergeometric functions.

u=3x²y+2x²-y³-2y² orthogonal trajectory Complex variables

Express the flowing equation in Cartesian equation r = 1-cos e

Eliminate the arbitrary constant a from the equation (z - a) + y = a° O = + 2ryy" O = + 2ry' Ov =r+ 2ryy O-r+ 2ry'

Find the equation of the osculating plane of the helix x = sin 2t, y = t, z = cos 2t at the point (0,,-1) by finding the TNB frame at this point. %3D

Determine order and degree * d'y + cos dr? d'y dr? 2 O 5 undefine- Not linear

Which of the following equations are homogenous or not : x³+y3 1. у' ху? 2. y' 3D еу + sin: y 3. dy =dx x+y 4. y' = x2 x+y 5. y' = X-y х-у+3 6. y' = х+у-1

A bee starts at the point (5, 7, -3) (with units in meters) and travels at a constant speed of 9 m/s in the direction of (1, -2, 2) for 10 seconds. A. Give a parametrization for the bee's position as a function of time. B. At what point does the bee end up?