Determine the longest interval in which the initial value problem is certain to have a unique twice differentiable solution. (Don attempt to find the solution.) (1 - 1)y" – 4ty + 5y = sin t, y( – 2) = 2, y ( – 2) = 1

Q: 2. Solve using any technique y" – 2y – 3y = sin r

A: First we find CF and then PI(by using the formula of PI of sin(ax)) and further find general…

Q: Find the general solution of the following equations (The answer can be given either explicitly or…

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Q: Find the general solution of y"+y = cos(t) (a) Using undetermined coefficients (b) Using variation…

A: Find the general solution of (a) Using undetermined coefficients.(b) Using variation of parameters.

Q: y" - 5y +by = 2 e² 11 zt

A: To solve the given problem, we have to apply the method of undetermined coefficients. Note:- From…

Q: Q5. Use the method of undetermined coefficients to solve (a) y" + 2y + y = x²e-". (b) у" — 2у + 5у 3…

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Q: Solve (y cos x – 3x²y – 2x)dx + (2y sin x – x° + In y)dy = 0 Solve x sec (ry)dy = -[y sec (xy)…

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Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: (b) y" – 2y' + 5y = eª cos 2x, y(0) = 2, y' (0) = –1.

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Q: Find a particular solution to y" +4y = - 12 sin(2t).

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Q: dy y(cos 2t)ety — 2(sin2t)ety + 2t + (t(cos2t)ety – 3)- dt = = 0, y(0) = 0

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Q: 1) Solve for r, 0 <x< 2n. sin (4x) – sin (2x) = 0

A: Given that: sin(4x)-sin(2x)=0              and             0≤x≤2π

Q: (f) y" - y' + 2y = 3e + 4 cos 2x

A: Consider the differential equation y''-y'+2y=3ex+4cos2x. To find the general solution of given…