Given that y(t)=c1(e^4t)+c2(e^(−4t)) is a solution to the differential equation y′′−16y=0, where c1 and c2 are arbitrary constants, find a function y(t) that satisfies the conditions y''-16y=0, y(0)=4, and lim (t->+∞) y(t) =0

Q: Solve: y''+ 6y' +5y = 20t + 39 y(0) = - 4, y'(0) = 19 | y(t) =

A: The solution is given as

Q: max value for y

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Q: Is f(x) If so, √2x+3 find differential at x = 1? f'(1)

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Q: First, use the substitution y₁(x) = e-5x. Y₂(x) = u(x)y₁(x) u(x)e-5x = Then, use the product rule to…

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Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: If R'(x)=250-18x and R(0)=0, find R(x)

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Q: x' y' 7x + 6y ||||

A: We have to find the value of x(t) and y(t).

Q: Suppose ay″+by′+cy=0 with y(0)=d and y′(0)=k has a general solution y=5e^(3x)−xe^(3x).   What are…

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Q: Note that y(t) = c1 + c2t + (t^(3) /6) is a general solution for y''= t. Find c1 and c2 such that…

A: Given equation is y''=t The general solution of the equation is given by  yt=C1+C2t+t36...........i…

Q: y(x) is the solution of the differential equation dy/dx = 4xy^2  when x = 0, y = -1 a) when x =…

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Q: Set up the appropriate form of a particular solution yp of the dif- ferential equation…

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Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

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Q: find all functions u(t) that solve the equation u'(t)+t*u(t)=-t * e^(-t^2), subject to u(0) = 1

A: Linear Diffrential Equations: The ordinary linear differential equations of the first order are…

Q: Find the general solution to (t² + 4)y' + 2ty = t²(t² + 4). Enter your answer as y = .... Use C to…

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Q: Solve y'' + 4y' + 4y = 0, y(0) = 3, y'(0) = y(t) = 9

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Q: y(4) = y(3) + y" + y + 2y and y(0) = y'(0) = y"(0) = 0, y(3) = 30. %3D

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Q: The general solution to: y'' – y' + 4y = 0 %3D is: y(x) = %3D Typle c_1 and c_2 to get c1 and c2 and…

A: We have to find the solution

Q: The function y = A e^(3x) + B x e^(3x) is the primitive of the differential equation y’’ – 6y’ + 9y…

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Q: Solve y’’ – 4y' + 40y = 0, y(0) = 2, y'(0) y(t) = = - 2

A: The given differential equation is y''-4y'+40y=0 with y0=2 and y'0=-2. We know that, if auxiliary…

Q: The solution of the Bemoulli equation y' +2-Vy= 0 is:

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Q: mit equatio x²y' + 2xy + O with respect to x and solve for y'. Skip (you cannot come back) x²y + xy²…

A: Given query is to find the derivative.

Q: G(y) = (y − 1)4 / (y2 + 2y)7 Find G'(y) =

A: for a polynomial function of power n: Division rule of differentiation:         Chain rule :…

Q: | 1) Find a function y whose graph passes through the point (1, ) and satisfies x²y' = y.

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Q: [Q3] Using the method of undetermined coefficients. (a) Solve y" - 2 y' - 3 y = 2e* -10 sin x, y(0)…

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Q: Solve y'' - 2y' + y = 0, y(0) = — 5, y'(0) = = y(t) = - 8

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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.