A mass weighing 4 pounds is attached to a spring whose constant is 2 Ilb/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 14 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ft

Q: mine the differential equation function whose general solution is the family 2x y = 1+206**

A: The solution a DE is given byClearly it has one arbitratry constant, hence the DE must be a first…

Q: Find the solution to the differential equations sec³ xdy = csc² y dx πT y (n) == 4

A:

Q: Find the solution of the Differential Equation (D³ - 3D²+4) y = 40cos2x+6

A: D3-3D2+4y=40cos2x+6

Q: Solve the differential equation x"(t) - 4x(t) = t using the factorization method.

A:

Q: -2r y=Ae²+ Be -2x-5e- y=Ae-2¹ cos(x) + Be-2¹ sin(x)

A:

Q: Find the general solution to the linear first-order differential equation: -+ dx 3x x²+1= 1 6x x²+1

A: The given differential equation,.The objective is to find the general solution to the differential…

Q: (y - 3y + 2)√9+ x²dx + x²dy = 0

A:

Q: find the general solution of the following differential equation x2D2y + xDy + 9y = 0

A:

Q: (D² + 1)y = sec² x csc x

A: Solve the differential equation by the method of variation of parameters : D2+1y=sec2xcscx

Q: Solve for c1 0 = C1e5 + C2e-1

A:

Q: d. y= x² + y x + cos y

A:

Q: x²y" - 3y² + 2y = 0

A:

Q: Find the solution of the following differential equations: Parallel Lines (2x + y + 1) dx + (4x +2y…

A:

Q: D² - 4D + 4)y= e²x sec²x (by Reduction of Order)

A: Solution :

Q: (D²+4)y= 4csc³2x (by Variation of Parameter

A:

Q: What is the general solution to the differential equation (3x+2y+4)dx+(3x+2y-3)dy=0?

A: An equation which involves the derivative or differential coefficient is called differential…

Q: Find a general solution to the differential equation r"+3r + 4x = 0.

A: To write the characteristic equation of x''+3x'+4x=0, replace x'' by x2, x' by x, and x by 1 in the…

Q: Use the above to solve the following system of differential equations: 31= x1+2x2 3/2 = 2x1 + x2

A:

Q: y= c, e2t + Cze-+

A:

Q: The solution of the differential equation 3+6 Y-7Y=0.

A:

Q: 2) Find the differential equation by eliminating the arbitrary constants A and B from B y = 5 Ax+ —…

A:

Q: Imagine the results of your experiment is an ordinary differential equation. x*dy + 4x3ydx = 0 a)…

A:

Q: What is the solution of the differential equation of (2x° + ry? + 2y +3) dr + (x²y + 2x) dy = 0 ?

A: We have given differential equation,   Differential equation is of the form,     Mdx +Ndy=0 Firstly…

Q: 4. Solve the following system of differential equations: x = x1+ x2+ x3 = x3 x = x1+ x2

A:

Q: y= C, e + Cze-2+

A: Formation of the differential equations

Q: Given any first-order differential equation, outline a process for determining an appropriate…

A: We have to give the process for determining an appropriate solution method.

Q: The general solution to an exact differential equation is an implicit solution. O True False

A:

Q: What does it mean when we say that two or more differential equations are coupled?

A: A differential equation is an equation that carries one or more functions with its derivatives. The…

Q: Write down a differential equation of the form = ay+b where all solutions approach y = dt as t → 0.

A: The given question is solved below.

Q: 1. (x² + y²)dx – xydy = 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.