If the system of differential equation has a chractristic equation 1² – 4A +4 = 0, then the general solution will be in the form

Q: Solve the differential equation (6D² +13D+7)y = e¯6x — 11x².

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Q: 2) Solve the differential equation: (D² – 11D + 28)y = 50 – e30x + e 4x

A: We have to find the general solution of given differential equation.

Q: Find all solutions of the z2 + 2z + (1 – i) = 0.

A: we have to find all solutions of the z2+2z+(1-i)=0 .

Q: Find a real general solution x2y"+0.7xy′−0.1y=0

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Q: Find the most general real-valued solution to the linear system of differential equations 12/2 x₁(t)…

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Q: rential equations f

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: Find the corresponding linearized system at each equilibrium point

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Q: 47x +75y -30x - 48y satisfying the initial conditions r(0) = 19 and ly' y(0) 12. x(t) = y(t) =

A: Given equations  are  x'=47x+75yy'=-30x-48y  with the initial conditions x0=19 and y0=-12 To find…

Q: -2 3 ㄴ X " dx ㅜ

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Q: (dx = x - y+z dt |dy = x +y – z dt dz — 2х — у dt

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Q: The differential equation that represent the following syster 1 -1 x, is 2 3

A: The given system is, This system can be written as, On differentiating equation (2).

Q: メ= 6X-24 =-2メ+3y

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Q: Find the general solution to the following system of differential equations, x = 5x1 – X2 X2 = 9x1 –…

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Q: -"(x) + 2»'(x) - 3v(x) =D -글 + 1 + 2r2 + 4r-1

A: Step:-1 Given that  -v''x+2v'x-3vx=-2x2+1x+2x2+4x-1 This is second order non homogeneous…

Q: The solution of the differential equation 3+6 Y-7Y=0.

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Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

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Q: Solve the system of differential equations. 1 -4] [xx()-1] X, X 0 = XI= 4 -7 2

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Q: Solve the differential equation(b and a are variables) (D2+4D+3)b=1+2a+3a?

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Q: Give a real general solution to the equation (D2 + 8D + 41)^3 (D + 7)^2w = 0 : (b) Give a real…

A: (a) Consider the given information, D2+8D+413D+72w=0   Replace D by and find the roots of the…

Q: Solve the system of first-order linear differential equations: x₂ - 6x₂-x₂+2x₂ x₂ = 3x₂-x₂ x₂ = x₂

A: The given system of first order differential equation is: x1'=6x1-x2+2x3x2'=3x2-x3x3'=x3 This system…

Q: Solve the differential equation (D² – 8D + 16)y = -3e4x by an %3D appropriate method.

A: Given: D2-8D+16y=-3e4x The auxiliary equation is: m2-8m+16=0 Now solve;…

Q: - u"(x) + 2u'(x) – u(x) = - +-x' + 5x – 4 - "(포) + 2»'(x) - 3v(x) =D -를 + 1 + 272 +4r-1

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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.