Find the longest interval where the initial value problem (t - 3) (t − 3)²y" — sin ty' + guaranteed to have the solution. -y = t², y(1) = 1, y'(1) = 2.

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

A: The solution is given as

Q: 4x y" - 5y + 4y = ¹, y(0) = 0, y'(0) = 10/3 e

A: Please find attachment

Q: Solve y" +5y' = (2x+1)e" -5x

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Q: Solve. y'' – 36y = et The general solution will be 6t 6t y(t) : cje + c2e +

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Q: 3. Solve using any technique y" – 2y/ – 3y = 3e",; 7 ", y(0) = 3, y'(0)

A: We have to solve given problem:

Q: 3. Solve y" – 2y' + 5y = 0, y(0) = 5, y'(0) = –3. %3D

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Q: Solve following DE x^(2)y"-7xy'+16y=0

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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: olve for y' 1. xy'-y=1-y'

A: Given xy'-y=1-y'Now lets take y to RHS and y' to LHS (Left Hand side)⇒xy'+y'=y+1Lets take y' common…

Q: Solve 2(cos2x)y' + ysin(2x) = 4cos4x 0 =< x < pi/2

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Q: Solve: y''' + 6y'" – y' - 30y = 0 y(0) = - 2, y'(0) - 15, y''(0) = 45 y(t) =

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Q: 2. Solve y" + 2y' – 3y = 3, y(0) = y'(0) = 1. II %3D %3D

A: given differential equation is linear non homogeneous differential equation with constant…

Q: y as a function of x if '(1) = −2. x²y" +19xy' +81y = x5,

A: Given that the differential equation is                                      To find 'y' as function…

Q: solve: y'' - 5y' + 4y = 20cos(2x) + 30sin(2x) y(0) = 1 y'(0) = 3

A: We have to solve the differential equation given below : y'' - 5y' + 4y = 20cos(2x) + 30sin(2x) ,…