A suitable substitution to transform the D.E. t dy – y dt = tydt into linear equation will be :

Q: Use the characteristics method to determine the solution for the equation d2y/dt2 + dy/dt +3y = 0.

A: Dear student we are write the ordinary differential equation so  we use the characteristic equation…

Q: Solve for an autonomous equation? dy/dt = f(y)

A: An autonomous first-order ordinary differential equation is an equation of the form

Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

Q: (dx — Зх — 2у dt dy 3D —х + 3у — 2z dt dz = -y + 3z dt %D (λ1, λ = 3, λ5)

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Q: dy dt t2

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Q: An object is moving along a path defined by the graph  x^2+y^2=18 Compute  dy/dy, if dx/dt=-2,…

A: According to the question:

Q: Verify that the function 5x3 + 3t4 is a solution to the 2nd order differential wave equation.

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Q: If the equilibrium of dy/dx = y - sqrt(y) when y>0 is y=1, is it a stable or unstable equilibrium?

A: Given dydx=y−y, when y>0 We have to check whether y=1 is stable or unstable equilibrium. Note:-…

Q: dz dS 2 If S = z3 and -2 when z = 3, find dt dt

A: Derivative

Q: Sketch the x and y nullclines, find the critical points and cassify, if poosible and use the…

A: Given the differential equation, To find the nullclines,

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

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Q: Can you help me step by step with this problem?

A: Apply exponent rule for the exponent then use chain rule Exponent rule: d/dx(x^n)=n*x^(n-1)Chain…

Q: Solve the following inital value problem  (dy/dt)=t2e-y  y(0)=1

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Q: what is the dependent variable and linearity of the DE: d(xy)/dx + xy=0?

A: We will find out the required values.

Q: y? what is dt/dy? 2y +1 if t =

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Q: -20 et 2. Let R(y) = dt. Find R'(y). DO NOT SIMPLIFY!!!

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Q: In Exercises , find the indicated derivatives.9. ds/dt  if s = t/2t + 1          10. dy/dt  if y = t…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Calculate dy/dt using the given information. xy2=4; dx/dt=-5, x=4, y=1

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Q: Find S t? e' dt using integration by parts.

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Q: If æ? + y? = 25 and dy/dt = 6, find %3D dæ /dt =

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Q: Find all solutions of the equation: dy​/dt=yt−y−t+1. Stationary and non stationary

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Q: 1 y' = 1– sint - y(t)dt, y(0) = 0 0,

A: Given the equation y' = 1-sin(t) -∫01y(t)dt. Initially, we integrate both sides of this equation…

Q: y = tan (5t - 21 +1)

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Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: The solution of the differential equation using dy + 6y = 7e-3t is dt Laplace transform „given that…

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Q: Find dv ifv = t- dt

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Q: 3. Use the phase plot for dy g(y) to identify the equilibria (if any) and their dt corresponding…

A: Step:-1 Given that dydt =gy and graph is Using above graph, we can see the graph touches and cuts…

Q: Find dy/dx

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Q: dr = x – y +t dt dy =エ+3y +t+1 dt (20, yo) = (-4, 5)

A: Given that, dxdt=x-y+tdydt=x+3y+t+1 This can be written by, X'=1-113X+tt+1 Now the homogenous eigen…

Q: d dt dx dy ruations dt - 2x +2y 1-2t, dyx-0. Giv dt 2 dt

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Q: Find dv if v = t- dt |

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Q: Compute the derivative: d I/ In(t° + 1) dt dx

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Q: What is an integrating factor of the DE dy/dx = (y + y^2) / x ?

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Q: dT equation dt k(T A).

A: we have been given the differential equation dTdt=k(T-A) this is the first-order linear differential…

Q: S(t)e¬Jwnt dt_ 2 C =

A: In this question, we find the coefficient for the Fourier complex series cn=2T∫0Ts(t)e-jwntdt

Q: Determine whether the given equation is separable, linear, neither or both.  (t^2+1)dy/dt=yt-y

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Q: If x'+y' +z-9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x,y,z) (2,2,1)

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Q: Calculate dy/dt using the given information. xy+x=12; dx/dt=-3, x=2, y=5

A: To calculate (d y)/(d t). find the slope of tangent line of the given curve by using implicit…

Q: dx 2x - y dt dy

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Q: Plot the phase line of the following equation and discuss its qualitative implication dy/dt = y2-y-6

A: Derivative of the function f(y) is the measure of how fast the function is changing with respect to…

Q: Find dy/dt. y =

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Q: If eSp e = p + t, compute dp/dt when p = t = 0. p'(0)

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Q: solve the simultaneois equation (dx)/(dt) = 3x + 2y (dy)/(dt) + 5x + 3y = 0

A: Given simultaneous equation, dxdt=3x+2ydydt+5x+3y=0 The eigen value of a matrix is calculated by…

Q: dy – 2ty = –31²e? dt - and the condition v(

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Q: The two functions y1(t) = sint cos t and y2 (t) = sin 2t are linearly Independent. True False

A: →Two functions y1 and y2 are said to be linearly independent,                 if, y1 ≠k y2 , where…

Q: t (a) y = dt Vt? +1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: zp dt

A: we have to solve the differential equation. dzdt+2et+z=0

Q: The order and degree of the differential dy equation + respectively, are O 2, 2 O 1,2 O 4, 2 O 2,1

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Q: Find the logistic equation that passes through the given point. dy/dt = y(1 − y/80), (0, 8)

A: Our Aim is to find the logistic equation that passes through the given point.dydt=y1-y80 and the…