The charge g= g(t) in the capacitor in an RLC circuit satisfies the differential equation da 800 dt g= 0, 200 For which value(s) of the resistance Ris the circuit critically damped?

Q: The rate of change of the height h(t) of water in a cylindrical tank with a hole in the bottom is…

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Q: Use an Integrating Factor to solve the differential equation.

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Q: - ysin)dn t x sint

A: See the details solution in below

Q: Find which direction field belongs to the differential equation dt dx = t2 – x. (You can explain by…

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Q: What is the differential equation for the population P(t) of the country when individuals are…

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Q: Verify that the function is a solution of the differential equation.

A: Given ,differential equation is:y''+y=0 Given function is: y=C1sinx-C2cosx Differentiating both…

Q: Match the appropriate slope field with the differential equation y'=+2. 事 B.

A: given differential equation y'=xy2+2 claim- to find the slope field of the given equation definition…

Q: Classify the differential equation as separable or linear (1+2*); dy = 4y dx

A: To classify the differential equation as linear or separable.

Q: The velocity v and time t are related by the first order differential equation below. Find the…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: cosy dx + (1 + e¯*)siny dy = 0

A: By separating the variables on each side  we can integrate them easily. Given, cosy dx+(1+e-x)siny…

Q: 6

A: Now,  we will find the particular integral.

Q: Write an equivalent first-order differential equationand initial condition for y

A: Given Data The equation is y=2-ꭍx0 (1+y(t)) sin t dt.   Differentiate the equation y=2-ꭍx0 (1+y(t))…

Q: This nonlinear differential equation, which describes wave mo- tion on shallow water surfaces, is…

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Q: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

Q: Solve the differential equation using Variation of Parameters e* (D² – 2D + 1) y

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Q: Let y=A cos x + B sinx is the solution of the differential equation

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Q: The differential equation of the form = sin x has a degree equal to dy %3D Enter your answer as a dr…

A: We have to find out degree

Q: Use separation of variables to find the solution to the differential dB equation + 2B = 50, if B(1)…

A: we have to solve the given differential equation by method of separation of variable.

Q: dx + (1 – x²) coty dy = 0

A: Given differential equation is,

Q: Match the differential equation with the appropriate slope field. y' = \ OA) B) |||||IVAA -411111 Y…

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Q: Write an equivalent first-order differential equationand initial condition for y

A: to find first order differential equation of y=∫1x1tdt

Q: Solve the differential equation. du 6 + tª dt ut? + u^p?

A: The given problem is solved below in detail.

Q: Form the differential equation by eliminating constants a and b from y = a(b – z)(b+1) + 52. %3D

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: For what value of is the differential equation (6zy + cos y) dr + (3ka²y? – 3y?) dy = 0 exact?

A: Exact differential equation

Q: Consider the differential equation x¨(t) + x(t) = 5t2 − 2 cos 2t.  Write down the ansatz for xp…

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Q: Determine the type of differential equation given below: * 2x(у + 1)dx — уdx %3D 0

A: Given differential equation  2x(y+1)dy - ydx = 0 If the differential equation is in the form…

Q: dy Vx ev+Vx¸ x > 0 %3D X dx

A: To Find the seperable differential equation

Q: Classify the differential equation d y d'y + tan x %3D da3 da5

A: Follow the procedure given below.

Q: Use separation of variables to find the general implicit solution to the differential equation. 9…

A: Given:       9 dydx=eysin2θysecθ

Q: Determine the differential equation that is satisfied by x(t) = c,e3t + cze¬t – te-t

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Q: Classify the given differential equation according to its type, order, degree, and linearity. du…

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Q: Find the current I as a function of time t (in seconds), given that I satisfies the differential…

A: Given differential equation is, LdIdt+RI=sin2t

Q: Solve the differential equation dy 2y-cotx tan? e dx

A: Given: tan2xdydx=e2y-cotx

Q: ly- cos? x) dx+ cos xdy = 0

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Q: Identify the order and degree of the differential equation: 1+ dx O a. 2nd order, Ist degree O b.…

A: We have to find out the degree and order of the given differential equation

Q: Use separation of variables to find the solution to the differential dB equation + 2B — 50, if В(1)…

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Q: dy Plot the slope field for the differential equation dx = y?- - x and sketch the solution for the…

A: Solution is given below:

Q: dx +x tan y= dy sec y 1+tan

A: The given differential equation is; dx/dy +xtany=secy/(1+tany)

Q: The amount u of a radioactive material change in time given as a differential equation du dt = -7u…

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Q: dy +2xy = e-* is The integrating factor of the differential equation

A: By using linear differential equations integrating factory  we can calculate..

Q: Solve using separable differential equations dx 3xt? dt

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Q: What should be A for the exact differential equation of ry + A 2Ay – x -dy y? Moreover evaluate the…

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Q: Xoly-yolx- Jrig? dXこ0

A: For checking the function is homogeneous or not , firstly we find dydx and then we calculate the…

Q: differential

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Q: Solve the differential equation below: dx=(x+e^y)dy

A: solution:-dx=x+eydydxdy=x+eydxdy-x=eysolving the first order linear differential…

Q: Find the solution to the differential equation  dz/dt=7tez that passes through the origin. z=?

A: We have to find the solutions

Q: Is the differential equation linear? y' = y + ey

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Q: Find the differential equation by eliminating the arbitrary constant/s. e COsX = c(1 – cos y) %3D

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Q: A small cannonball with mass 9 kilograms is shot vertically upward with an initial velocity of 130…

A: we have m=9, v=130, k=0.0025, g=-9.8