Which of the followings is the correct choice of "k" for which all solutions of the differential equation remain finite as t → 0. y" + (3k – 1)y' + (2k – 1)ky = 0 O A )k<0 O B)k >0 O "k2 O Dk>0 O Eks

Q: 1 - 2 9) Ans. r = 1

A: Given the matrix . We need to find it's rank. As we know that rank of a matrix is number of non zero…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: y=Ae5x+Be6x

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Q: Use the transformation u = v = ryto find || xy dAover the region Rin the first quadrant R enclosed…

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Q: For what value(s) of r does the function y = e satisfy the differential equation "+9y +18y 0. %3D…

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Q: Consider the differential equation 4y" – 4y' – 8y : 8 Find a particular solution - e* for the given…

A: Solution given below

Q: Which of the following differential equation has a solution of y = e"(c, cos 2x + c, sin 2x) ?

A:

Q: y" - 2y' = -4 y(0) = 0, y'(0) = 4

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Q: The singular points of the differential equation xy"+y+ O a none Ob0,-2 Oc. 0, -2,4 O d. 0,4 Oe0…

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Q: Provide a general solution formula for the differential equation y" – 15y" + 70y" – 120y' + 64y = 0,…

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Q: II. Find the differential equation by eliminating the arbitrary constant/s. 1. y-¹ = x(3e* + c) 2. y…

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Q: a) 3dy = sin(x)(y² – y)da dy + (x + 5)y= 5xe 2 dx

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Q: –3x Show that the function y= e²* + e* satisfy the differential equation y"+y'-6y=0

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Q: 3. 6y" – 7y' – 5y = 2x + e-5 [5 marks]

A:

Q: EC2: Verify that y₁ = 2³ and y., = |aare linearly independent solutions of the differential equation…

A: Two solution are said to be linearly independent if neither function can be put as a constant…

Q: Which one is the differential equation if its solution is y= acoSx-bsinx O a. y"-y' 0 O b. None of…

A: To find the differential equation whose solution is represented as: y=acosx−bsinx

Q: (6): Partial Differential Equation Solve the following equation do/dt-h² d'o/dx²2 0 (x, t) LC t=0…

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Q: Solve the differential equation by variation of parameters. 2y" - 4y + 4y = ex sec x ex(c₁cos(x) +…

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Q: Solve the differential equation y"-3y'-4y 0 O y= e3* (c cos 2x + C2 sin 2x) cos 3x + c2 sin 3x) O y=…

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Q: Which of these are singular points for the differential equation x-6 x + 4 Select all that apply.…

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Q: Consider the differential equation 4y" – 4y' + y = 0; eX/2, xeX/2. Verify that the functions ex/2…

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Q: Which one of the following differential equation is the Bernoulli's form of differential equation?…

A: Bernoullis differential equation

Q: Match the differential equation with its direction field. y' = 2-y

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Q: A differential equation ay" + by" + cy' + dy = 0 where {a, b, c, d} are constants has the roots of…

A: Topic :- Differential equation

Q: 4. Solve: y³ dx + (x-1) dy = 0 1+2y In |x-1|=ky²2 1-2 y² mm |x-1|=ky² 1-2y In x + 1) = ky 1-2 y ln…

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Q: Let y'= 2xy²; y = a. (-4,4),(-∞, -4] b. (-4,4) c. (-4,00),(-4,4),[4, ∞) d. (-4,00),(4,∞), e. (-∞,…

A: Given,  y'=2xy2 and y=24/(x2-16)

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A: We have to find the solutions

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.