Find y(t) solution of the initial value problem y" - 6y' +9y= u(t - 2) e-³(1-2), y(0) = 0, y'(0) = 0, where u(t) is the step function.

Q: 23. (x+1)(x-2)y' + y = 0, y(1) = −3

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Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: Consider the following (x²-3x+1)y" -(x²-x-2)y'+(2x-3)y=0 on the interval I = (3,00) Verify that Y₁…

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Q: SOLVE In(x)y' - y = In² (x) ; y(3) = 1

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Q: Solve y'" – 4y' + 20y = – 68e*, y(0) = 0, y'(0) = 0| - y(t) :

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Q: Find the solution to  x' = y - x + t y' = y if x(0) = 2 and y(0) = 4 x(t) = ? y(t) = ?

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Q: 8.) y" +2y' +5y = 3e 2* ; and y(0) = y'(0) = 1

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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: Solve the initial value problem given by y' = (x2 + 2y2)/(xy) ,  y(1) = 1 What is the interval of…

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Q: 5. Find a particular solution to the equation -2x y" + 4y' + 4y = xe¯

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Q: Solve u' (t) + u(t) = 5 subject to u (2) = -2. 85 Provide an exact expression (i.e. no decimal…

A: Question - solve u'(t) + u(t) = 5 subject to u(2)=-2

Q: Solve (1 07 y'' – 4y' + 3y y(0) = y'(0) = 0 y(t) = f(t)uo(t) - g(t)u7(t), where f(t) = g(t) =

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Q: Solve: y'"' + 4y'' + 5y' + 2y = 0 y(0) = 4, y'(0) y(t) = = 4, y''(0) = 5

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Q: Solve y'' - 4y' + 29y = 0, y(0) = 3, y'(0) = y(t) = 9

A: The given differential equation is; y''-4y'+29y=0, y(0)=3, y'(0)=-9.

Q: 2. Use separation of variables to solve (a) y' = -2y, y(0) = 1 (b) 4y' = y², y(0) = 4 %3D (c) y' + y…

A: Note:  "As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Use undetermined coefficients to find the particular solution to y''+ 7y' + 10y = 3e Y(t) =

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Q: Use substitution method

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

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Q: Find the longest interval where the initial value problem (t - 3) (t − 3)²y" — sin ty' + guaranteed…

A: Given the differential equationThe objective is to find the largest interval on which the initial…