Verify that the given equation y²dx+zdy+ydz=0 a) If the equations is found to be exact b) treat one of the variables as constant c) If the equation is Homogeneous Pfaffian Differential Equation
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- 4. The equation of motion of a particle is s = t* – 2t3 + t2 – t, where s is in meters and t is in seconds. a) Find the velocity and acceleration as functions of t. b) Find the position, velocity, and acceleration after 1 second.Find the Integrating factor of: dy + у. sec5x tan5x dx 1 (sec5x + tan5x) 5 sec5x — tan5х + 5 O sec5x + tan5x O Nonelinearise R = AT + BT2
- verify that w xy = w yx . w= (3x - y)/(x+y)dv =-(av+bt), where a and dt 6. The equation b are constants, represents an equation of motion when a particle moves in a resisting medium. Solve the equation for v given that v=u when t=0.Two electrons repel each other with a force that varies inversely as the square of the distance between them. One electron is fixed at the point (2, 4). Find the work done in moving the second electron from (−2, 4) to (1, 4).
- Without solving, classify the following equations as to: separable, homogeneous (the degree), exact, linear, Bernoulli, or Ricatti (d) y + 5y? + 2ry = 3r*. %3D dy (e) y dr +r dy - 0. (f) = () y dr = (y- ry²) dy(h) r dy ye/y. - r.If ø = 4xy, find x and y components of the velocity at (1, 4) and (4, 4). Calculate the discharge passing between the streamlines passing through the points.When you cough, you are using a high-speed stream of air to clear your trachea (windpipe). During a cough, your trachea contracts, forcing the air to move faster, but also increasing the friction. If a trachea contracts from a normal radius of 3 centimeters to a radius of r centimeters, the velocity of the airstream is V(r) = c(3-r)r2 where c is a positive constant depending on the length and the elasticity of the trachea. Find the radius r that maximizes this velocity. (X-ray pictures verify that the trachea does indeed contract to this radius.)
- 2 Suppose that A = 3xyz² + 2xy³jr²yzk and = 3x² - yz. Find, at the point ¢ (1, −1, 1), 2.1 Vo, 2.2 V. A, 2.3 A. Vo, 2.4 V · (6Ã), 2.5 V. (Vo), 2.6 Directional derivative of in the direction of A, (0) 2.7 V × Ā, 2.8 (Vo) x A, 2.9 V X (A).Show that V. (V x A) = 0.a) The specific volume v of a gas can be expressed as a function of its pressure p and temperature T, as; KT p=- v -b a where Kis the gas constant, and a and b are constants. Show that the equation can be re- arrange into, f(v) = Av³ – Bv + Cv–D=0, where A, B, C, and D are constants. Using Newton-Raphson method, find the specific volume v of the methane gas at a pressure of 2.1162 x10'lbf / fi² and temperature 459.67° R with a= 4787.4 ft* – Ibf / lbm2, b = 0.0496 ft / Ibm, and K = 96.35 ft – lbf / lbm -° R. Use the starting value of v = 0.0 and accuracy of ɛ = 0.001.