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.

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A: Given: yx=C1x+C2-13x2 To find the values of C1 and C2 such that y1=1 and y'1=-1.

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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: (B) Find the general solution of x²y" - (2a-1)xy' + a²y = x²+¹ where a is a constant. Good Luck

A: This question is about ordinary differential equation.

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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: a)Solve the ecuation y''+3y'=12x-5 symbolic b)Solve the initial value problem y''+3y'=12x-5 where…

A: The given function differential equation is  y" +3y' =12x - 5 y(0) = 1,     y'(0) = 0

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

A: Given:

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Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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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

A:

Q: x²y"-9y" + 6y' - 9 = x² + 6x y'(0) = 0

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Q: The general solution to: y'' – y' + 4y = 0 %3D is: y(x) = %3D Typle c_1 and c_2 to get c1 and c2 and…

A: We have to find the solution

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

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

Q: xy' + 2y = 3x, y(1) = 5 %3D

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Q: What is the particular solution of y'=x²-2x+3, ify=4whenx=0?

A: What is Ordinary DIfferential Equation: A differential equation having one or more functions of one…

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: - Sapotri to solve 2x?y" – my + (x + 1)y = 0. n=0 12) Use y =

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

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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.