Consider the following initial value problem: y" + 6y' + 8y = 8(t — 5) + u₁0(t); y(0) = 0, y'(0) a) Find the solution y(t). y(t) = where c= + + and d = || = 2 uc(t) ua(t)

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Q: If y(x) is a solution of (1-2-2xy +42y = 0, find the value of y'(1).

A: It is given that yx is a solution of 1-x2y''-2xy'+42y=0. The objective is to evaluate y'1.

Q: particular solution

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Q: Find the solution to y '= 3y satisfying y(2) = 1000.

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Q: The general solution to y'' - xy' + y = 0 is given by:

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Q: Use the convolution to write a formula for problem: y" + 25y = f(t), y(0) = -2, y(0) = 1. |

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Q: Find the general and particular solution of the y"=3e³x if f(2)= k and f'(2)=k²

A: y"=3e³x if f(2)= k and f'(2)=k²

Q: Show that y = 5x2 + 2 is a solution to the DE xy' +(2)/(5) y" = 2y.

A: To show: y=5 x2+2 is a solution of differential equation xy'+25y''=2y

Q: If y is a solution of y"+xy'+3y =0 then find the

A: Find y' and y'' from the equation y=∑m=0∞ amxm .                                       y'=∑m=0∞…

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A: We have to find the solution to the given equation.

Q: Eliminate the constant: 3r y=c₁₂e²²+c₁₂e² Oy"+y'-6y=0 Oy"+ 5y¹+6y=0 Oy"-5y¹+6y=0 Oy"-y'-6y=0

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Q: Use undetermined y"-9y 3e* Y (t) = %3D

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Q: 3. Find the solution of the DE 2yy" = 1 + (y')², x > 0, y > 0.

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Q: If r(y) = e³y² +3 find r'(y) =

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Q: Find the solution of y" – by' + 9y = 16 et with y(0) = 2 and y' (0) = 1.

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Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: (Dー)y=0 findyc

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Q: (D3+25D)y=32cos24x and y(0)=y'(0)=y''(0)=0   find y(x)  regards

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Q: Consider the following equation: x?y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 1. Verify that y, (x) = x…

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Q: Consider the equation y' + 5y = 2. Show that the function o given by: %3D 2 $(x) is a solution,…

A: Given y'+5y=2 We have to find ∅x

Q: Find the general solution for the problem in the form y=yc+yp y'' - 3y' - 4y = 2 + 6t + cost

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Q: Find y as a function of a if y" − 3y" − y + 3y = 0, y(0) = −9, y'(0) = −8, y'(0) = 7. y(x) =

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