determine the nature of the critical point and draw the phase plane of x'=Ax d) e) (-2-3) 3-4 1 -1

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A: Given  The differential equation is y''-2y'+y=0

Q: 3. t(t-4)y" + 3ty' + 4y = 2, y(3) = 0, y'(3) = -1

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Q: t²y' + 2ty - y³ = 0

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Q: Find a particular solution to y" + 4y' + 3y = -16te²".

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Q: For each equation draw a phase line (label the axis) labeling all critical points and their…

A: (a) Given the DE dydt=-y3+3y2-2y.

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A: Given differential equation is t2y''+5y'+(t+2)y=0   Also, given y1, y2 are Linearly Independent…

Q: Obtain two linearly independent solutions valid near x = 0  xy" + x(x - 1)y' + (1 - x)y = 0

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Q: Are y₁ (1) = x, y₂(x) = ze² a fundamental set of solution for the equation r²y" − x(x + 2)y' + (x +…

A: Given thatand  are two solutions of DE

Q: Question 2 Differentiate y = In(3x – 2x). %3D - 12z3-2 O y'= |3D 3z4-2r 12x – 2 |3D dz 3z4-2z 1 O y'…

A: Explanation of the answer is as follows

Q: solve the deq by method of substituiton

A: The given differential equation is 2x+y+4dx+x-2y-2dy=0......(1) We shall solve the differential…

Q: show that the solution y(t)=e^2t(cos(t)-2sin(t)) is linearly independant.

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Q: Eliminate the constant: 3r y=c₁₂e²²+c₁₂e² Oy"+y'-6y=0 Oy"+ 5y¹+6y=0 Oy"-5y¹+6y=0 Oy"-y'-6y=0

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Q: Obtain the particular solution 1. (D³ +6D² + 12D + 8)y=0 when x = 0, y = 1, y'= -2, y" = 2 2. y" +…

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Q: y" + 4y' = 3sin2t + tcos2t %3D

A: The solution for the above question is as shown below.

Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

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Q: show that the solution y(t)=e^2tsin(t) is linearly independant.

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Q: - choose the correct answer If y = t^2/(t^2+1) and t= v(2x+1) the = dyldx %3D 1/N(2x+1) O 2(x+1)^2 O…

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Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

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Q: Find dx * and then simplify whenever possible. dx2 1) y = 3t5 – 2t x = 4t3 2) y = t-3 – 7 x = t? –…

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Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

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Q: y" + 2y' + 4y = 0

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Q: Consider the DE dy/dt = y^(3)*(y −1)2(y + 2). Draw the phase line and a graph showing the long-term…

A: This is a problem of the autonomous differential equations.

Q: Write the equation „dr te +x dt dr in the form of +p(t)x=q(t). Then identify p(t) and q(t). dt…

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Q: Find the general solution of the Bernoulli equation 2yy′= y^2+ t + 1.

A: To solve given differential equation first we solve for rearrange the equation in the form of first…

Q: DE dx dt = x² - 4x + 3. (a) Its stable critical point is X = unstable critical point is X =

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Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

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Q: Obtain two linearly independent solutions valid near x = 0  x(1 - x)y" - 3y' + 2y = 0

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Q: Find the annihilator:  f(x) = cos(2x) +4sin (3x)  a. (D^2 +3)^2  b. (D^2 +9)(D^2 +4) c. D^2 - 4D…

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Q: Find two linearly independent solutions of 2x²y" - xy' + (-1x + 1)y=0, x > 0 of the form y₁ = x¹(1 +…

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