A nonhomogeneous linear differential equation has the following form: an (x) ym) + an-1 (x) yn-1)+...+a2 (x) y" + a1 (x) y' + ao (x) y = g (x) Determine g (x) in the following equation: y" – y' +3y = 2 cos r +3 sin 2x O 3 sin 2r O 2 cos z +3 sin 2x O 2x O 2 cos z

Q: Consider the first-order differential equation for y(x): dy = y tan x + sin x . dx du find a…

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Q: Identify the exact differential equation. O (1+ y?) dæ + (1 + 2y) dy = 0 %3D O sin 3x da + cos 3x dy…

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Q: Determine the order of the following differential equations: xy = 1 y" +x*y' = 2 (b) (y)3 +x 1 (d)…

A: The order of a differential equation is the highest derivative present in it.

Q: 8.) Match the following differential equations with their phase portraits A.) x" + 10x' + 24x = 0…

A: Differential equations as it's phase portraits given below

Q: Evaluate the given differential equation cosy sin2x dx + ( cos²y – cos x)dy = 0 A. cos x (1+ siny) =…

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Q: 3. Solve the differential equation subject to the given conditions. d² y dx² a) b) d² y dx² +36y= 0,…

A: As you didn't mention the question number to be solved so I solved two questions. For remaining…

Q: Find the general solution of y' =y sec x. A. y = C (secx+ tan x) B. y= C (sec x – tan x) C. y = C…

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Q: Find the solution to the given equations: (a) y" + y' – 2y = cos(x) – 3 sin(2x), y(0) = 1, y'(0) = 2…

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Q: Match the differential equation with its direction field. y' - 8(x + y) - 1 -0.3- -0.2 0.1 0.1 - 0.2…

A: Matching the differential equation with its direction field  y'=8(x+y)-1 x 0 0 0 0 0.1 0.2 0 1/8…

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.