State the order of the given ordinary differential equation. (sin(0))y"' - (cos(0))y' = 5 Determine whether the equation is linear or nonlinear by matching it with the given equation. + an – 1(x)" - ly dx" )dy + a1(x)- + ao(x)y = g(x) +... dx" dx - 1 O linear O nonlinear

Q: Use an appropriate substitution (4-5 a cos² to solve the differential equation (-) ) ª dx - x dy =…

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Q: solve y"cx) + 4 y(x) = 6 sin°(x) Find general solution of differential equation:

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Q: y = C, cos 3x - C sin(-3x)

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Q: Sove the differential equation given the condition y(0)=6   dy/dx = (x/y)

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Q: (a) 2xy? + x²y' = y², y(1) = = -1 (а) Зу(2? — 1) + (»3 + 8y — За) dy (b) 4x?3 dy гу* + 2 dæ (e) xy'…

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Q: : xydx - (x + 2y)2 dy = 0

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Q: Determine whether or not y=C1 cos (2t) + C2 sin (2t) is the solution to the differential equation…

A: we check y=c1 cos(2t)+c2sin92t) is the solution to the differential equation y''+4y=0

Q: Solve the differential equation by variation of parameteres: y'' + y = sec(x) + tan(x)

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Q: Evaluate the general Solution to the differential equation: Cy-cos-x)dx+ cosxody A y(secx + tan x) t…

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Q: State the order of the given ordinary differential equation. (1 – x)y" – 7xy' + 5y = cos(x)…

A: Order of differential equation: The order of the highest order derivative involved in a differential…

Q: The graph of the function f(x) is Given the differential equation x'(t) = f(x(t)). List the constant…

A: The given differential equation is, x't=fxt. The equilibrium solutions occur whenever x't=fxt=0.…

Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

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Q: Solve the differential equation y" = e" (y')"

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Q: 1 – 2xy)y' = yly + sinx] ; when x = 0, у %3D 1 + cosx 1+y²

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Q: Solve the differential equation: dy/dx=cos(x+y) when x=0, and y=pi/4

A: Solve the differential equation, using substitution method

Q: A tank contains 13 gallons of water to start, 9.5 gallons of water flow into the tank while 6…

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Q: Solve the exact differential equation ( - 2 sin(x) – y sin(x) + 4 cos(x))dx + (cos(x))dy = 0 where…

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Q: a) Solve differential equation dx + 2 dy x³ cos y %| - y

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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.