A steel ball of mass 4-kg is dropped from rest from the top of a building. If the air resistance is 0.012v and the ball hits the ground after 2.1 seconds, how tall is the building? Answer in four decimal places.   DIFFERENTIAL EQUATIONS

Q: у" - 9y' %3D 27

A: The solution are next step

Q: A ball is thrown from a height of 67 meters with an initial downward velocity of 5 m/s. The ball's…

A: The given equation is ht=67-5t-5t2. It is known that, the height h=0 when the ball hit the ground.…

Q: A cup of hot coffee initially at 100°C cools to 40°C in half an hour while sitting in a room of…

A:

Q: dy dx 2₁ y x = x + 2√/ X X

A:

Q: olve the d

A: Given,         dxdt=37.5-3.5x

Q: 8. (x – 3y) dx + (3x – y) dy = 0; y(0) = 2

A: Homogeneous Differential Equation: A differential equation of the form f(x, y)dy = g(x, y)dx is said…

Q: (b) The overall distance (in m) traveled by a golf ball is tested by hitting the ball with the golf…

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Q: (a). 2t²u" + 3tu'- u = 0,t> 0

A: The given differential equation is,let us substitute t=ez so z=logt and hence

Q: 3/xyy' = 5

A: We have to solve the differential equation  3xyy' = 5.

Q: 4xi4=*

A: Order :-The order of a differential equation is the order of the highest order derivative involved…

Q: 2: [3x +y =y«*]dx + [r* + 3y² +c=]dy = 0 3. 2х

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Q: 1 – 2xy)y' = yly + sinx] ; when x = 0, у %3D 1 + cosx 1+y²

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Q: Evaluate L {e-3(1-2) - 1¹e³¹ − 21²cos(2t) + 3e¯'sin(3t+ π) +-π)}

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Q: sistance R (ohms) and the current I (amperes) by the equation P = R1². se differentials to determine…

A: In this question, the concept of the derivative is applied. Derivative A derivative can be used to…

Q: PLEASE ANSWER ITEM NUMBER 10 ONLY. DIFFERENTIAL EQUATIONS.

A:

Q: Solve the homogenious differential equation Cy²+4y+4y=0; ylo)=1, y'(0) = 3 2 2 ⑤[ +² D² + 5 + D…

A: The homogeneous  differential equation is:The aim is to solve the homogeneous differential equation.

Q: 2. Coasting battleship Suppose that an Iowa class battleship has mass around 51,000 metric tons…

A: Mass, m = 51,000,000 kg K = 59,000 kg/sec vo = 9 m/sec So, v = vo e-(Kt)/m =  9 *…

Q: 21. 22. (D' + D - 9D' – 13D² + 8D + 12)y 0. Ans. y Ce+cze

A: We will solve the given differential equation.Below find the solution in the image.

Q: y = Cje² + C2xe* + C3x²e* %D O y" + 3y" + 3y' + y = 0 y" – 3y" + 3y' + y = 0 %3D + 3y" + 3y' – y = 0…

A: Given data is: y=C1ex+C2xex+C3x2ex

Q: 2. 2x sin? ydx – (x² – 9)cos ydy = 0 -

A:

Q: III. Homogeneous DE 1. x dy + (y – 2x) dx = 0 2. (2x + 3y) dx + (3x + 2y) dy = 0 3. 3(x2 – y?) dx +…

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Q: aur + 2xyury + y*uyy = 0

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.