Find the general solution of the system z' = x – 2y, y' = 2x + y. (3) +이(1)~ X = C1 + c2 est -sin(2t) est cos(2t) cos (2t) X = c1 et + c2 -sin(2t), O none of these -cos(2t) -sin(2t) -sin(2t) et X = c1 et + c2 -cos(2t) X = C1 cos (2t) (-sin(2t) et + c2 et X = C1 + C2 e3t X = c1 -2 e2t et + o

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A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

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Q: Consider the following IVP: у" +у'%3D-сos x;B у(0) %3D а, у(0) -b Find the general solution. A y (x)…

A: Solution of the differential equation

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A: according to our guidelines we can answer only three subparts, or first question and rest can be…

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A: We use derivative of u/v=( v derivative of u - u derivative of v)/v2.

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A: The matrix form of given system of differential equations as follows

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Q: Using variation of parameters, solve the nonhomogeneous system X'= AX + g, where 1 A=[24] g=g(t) =…

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Q: (2) Sketch the direction field associated to the system I'=x²-y-3, y = y + x² - 5. Include the…

A: sketch the direction field associated to the system    x' = x 2 - y - 3 y' = y + x 2 - 5   include…

Q: If Var(X+Y)=5, Var(X-Y)=2 and E(X)=1 and E(Y)=2 then Cov(X,Y)= (3/4 (1/4 (4/B

A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: Use D-operator methods to solve (1) (0²+16)y= tsint Cii) (D²+D+5)y =t coszt %3D

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Q: 42+2 312-5x Differentiate: y = O y = 12z-40z+12z-10 (3z2-5z) O y' = - 12z* – 40x³+12z–10 (3z2-5z) O…

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Q: olve: y" +10y" + 29y' = 0 Dy=C₁+C₂e-2 cos5x + C3e-2 sin5z Oy=C₁+C₂e cos2r + Czez sin2z Dy=C₁+C₂e-5…

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Q: x - ; )* ( sin 2t X' |X + 4 2 \2 cos 2t)

A: We have to solve the system of equations.

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Q: (2) Consider the following vector ODE 2 1 1 Y': × - (D) - - () 0 2 -1 Y + 0 0 0 -1 (a) Convert it…

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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.