The function y(x) = x³ – is a solution of which of the following initial value problems? (a) ry' + 3y = 6r³, y(1) = 0 (b) xy' + 3y = 0, y(1) = 0 (c) ry +3y = 6x-³, y(1) = 0 (d) ry' + 3y = 0, y(0) = 0.

Q: Q3/ Solve the following equations: 1- х(2у — 3)dx + (x2 + 1)dy %3D0 dy 2- dx 4y x (у-3) 3. y' = 2xy…

A: Note that there are so many ways to write the final answer of the differential equation.

Q: Find a general solution to the following higher-order equations. (a) y'' - 5y'' +6y' +12y=0 (b)…

A: The given differential equations, a) y'''-5y''+6y'+12y=0 b) y'''+3y''+y'-5y=0 c) y'v+13y''+36y=0 We…

Q: The unique solution to the initial value problem is y(t) = 2e-5t - 8t – 5. Determine the constant yo…

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Q: c. y' + 2y = x³ with y(1) = 2 Yo (x) = e Yp (x) = y (x) = y (x) = -2x 1½ e ²x³ - 2/ ( 10²x² -…

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

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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: The unique solution to the initial value problem is y(t) = 8e-5t - 2t + 9. Determine the constant yo…

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Q: Find the general solution to the following: (a) 6y"+y'- y = 0. (b) y" + 8y' + 16y = 0. (c) y" + 2y'…

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Q: Use undetermined coefficients to find the particular solution to y'' + 3y' + 2y = 4e - 2t Y(t) =

A: Given:

Q: (h) xy" + 8y' +18xy = 0, xo = 1 (i) (3 — x²)y" — 8xy' - 18y = 0, xo = 0 (j) 2y" + 8xy' + 18y = 0, xo…

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Q: Use undetermined coefficients to find the particular solution to y'' + 2y' – 4y = 2t + 2 Yp(t) =

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Q: 2. Use separation of variables to solve (a) y' = -2y, y(0) = 1 (b) 4y' = y², y(0) = 4 %3D (c) y' + y…

A: Note:  "As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: 4 y'+− y = 2; y(1) = −4 {y= X 2 = 5 -x-- 22 X 5

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Q: (a) y" – 4y" + y' + 6y 0. (b) y" – y" + 2y' = 0.

A: General solution for the Homogeneous differential equations with constant coefficients

Q: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

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Q: 2) Find the general solution to 2y" - y' - 6y = 0. Find the particular solution that satisfies y(0)…

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Q: The general solution of the 3rd order equation y′′′ − y′ = 0 is given by y(x) = C1x + C2e^x +…

A: It is given that is a third order linear ordinary differential equation. We have tofind the general…

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.