Solve the initial value problem y" + y' — 12y = 0, y(0) = a, y′(0) = −36. Find a so that the solution approaches zero as t → ∞. a

Q: Solve y" – 2y' – 3y = 3t² – 5 using the Method of Undetermined Coefficients.

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Q: Solve the initial value problem: 0 2 y = [ -2 -1 ]y, yo = [²] y' y(0) -2 2

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Q: Solve this separable equations starting from y(0) = 2:  (1 + x)y′ = 2y

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Q: Find the general solution to y''-1=0

A: y''-1 =0y'' = 1y' = ∫1 dxy' = x + By =∫(x + B) dxy = x22 + Bx + A

Q: The unique solution to the initial value problem is y(t) = 9e−²t + 4t + 7. Determine the constant y…

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Q: dy Solve the initial-value problem for y as a function of x. (16-2²) d = 1, y(0) = 9 y +9 X

A: The given initial value problem is:

Q: Find a particular solution to the given higher-order equation. y'"' - y'' - 22y' +40y = - 40t²…

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Q: 3. Solve each equation. y(0) = 1, y' (0) = -1 (a) y" + 4y = 0, (b) y" + 5y = 0

A: We have to solve given problem:

Q: Verify that x(t)= C1et+C2 is a solution to x"-x'=0. Find C1 and C2 so that x(t) satisfies x(0)=10…

A: The given differential equation is given by,

Q: Find the general solution y''-y'-2y=0

A: Given the differential equation y''-y'-2y=0. We need to find the general solution of the above…

Q: Solve the nonhomogeneous equation? .3. x*y" + x²y" – 2xy' + 2y = x³ In x. -

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Q: 1. Solve the equation y2 + 6x = y(3y – 2x)y'

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Q: Solve by undetermined coefficients. y" – 3y' = 6e – 2e", y(0) = 0, y (0) = 0.

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Q: Verify that the function y = c1e (-k+2t)x + c2e (-k-2t)x is a solution to y " + 2ky'+ (k 2 + 4)y =…

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Q: ) Verify that y=e-2x is a solution of equation x(y")3+ (y')4 – y = 0

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Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: [  y'''- y' = ex - 2x  ] Please find a particular solution yp for the above.

A: Particular Solution: Consider the equation Let be the differential operator Then equation (1) can…

Q: Solve 2yy′ + 1= y2 + x, with y(0) = 1

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Q: Find the solution of y' = (1 – 4x) y², y (0) = –1 in explicit form

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Q: Solve the give differnetial equation by undetermined coefficients y''' - y'' -16y' + 16y = 5 - ex +…

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Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 0