(9) Verify that Yp = sin 2x is a solution of y"– y = -5 sin 2r and use it to find the general solution.

Q: Eliminate the arbitrary constant for y = 2 + Cq sin 4t

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Q: Find a result by using undetermined coefficients for ý + y = x² + x+sin(2x)

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Q: Solve for the particular solution of y' = 1/1 e 42 +3 sin 2x when x = 0 and y = 1

A: The differential equation is given by y' = 12e4x+3sin2x The initial condition is  y0 = 1 To…

Q: Verify if y = c, sin 3x + c2 cos 3x + 9x2 - 2 is a solution to y' +9y = 81a?. Show your solutions…

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Q: Solve y" – 4y' + 8y = e2" + sin 2x 3.

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Q: Q1 show that fx=|x|sinx and gx=xsinx are independent solutions Q 2 Show that fx=|x| and gx=x ^2 are…

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Q: 2. (Dª + 4D²) y = 48x + 96 sin 2x

A: Given: D4+4D2y=48x+96 sin 2x   Solution: A linear non-homogenous ODE with constant coefficients has…

Q: Solve (D2+1)y=sin x sin 2x

A: Note that the particular solution can be obtained using the following forms: (i)…

Q: Solve for x sin(3x+10)=cos(x+24)

A: We have to find the value of .X

Q: Solve (D² - 2D + 5) y = sin (2x) + 17x cos (2x) — 15x -

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Q: Solve the general solution y4 + 2y" + y = x² sin x

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Q: Verify that y = cos x and y = sin x are solutions of the DE y” + y = 0. Are any of the following…

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Q: Construct an equation such that y = = C1e3z cos x + C2e3ª sin x is its general solution.

A: To determine the differential equation from the solution  Check the number of constant in the…

Q: Solve (D2+1)y=sin x sin 2x

A: The given differential equation is  (D2 +1)y = sinx. sin2x

Q: Find all solutions cos(4x) = cos(6x)

A: The objective is to find all solutions of cos(4x) = cos(6x)

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.