Use variation of parameters to solve the given system sin 2t x² = (2-1)x - (₂002)¹ X' (4 + Je4t cos 2t x(t) = c₁ [cos (2t),2 sin ( 2t) ] et + c₂[sin(2t), — 2 cos (2t)] + e[cos (2t), 2 sin(2t)]

Q: Determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. y" +…

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Q: Show that an implicit solution of 2x sin²(y) dx - (x² + 18) cos(y) dy = 0 is given by In(x² + 18) +…

A: Given that  Equation : 2x sin2(y)dx - (x2+18) cos(y) dy = 0 and Implicit solution : ln(x2+18)…

Q: The solution of (e +2ay) daæ + (2 cos 2y+ 2x?y) dy is given by (A) e" + a?y² + cos 2y = c (B) e +…

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

Q: The general solution of y" + y = e + 5e2* is y = ei (A cos (*) + B sin )) + Ce-" + 응e2x 2 () V5z y =…

A: Given that  y"'+y=e^(-x)+5e^(2x) To find the general solution

Q: y" + 4y = 2 sin 3x + 3 cos 2x Find the solution y(x)

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

Q: The solution of (e+2xy?) dx + (2 cos 2y + 2x?y) dy is given by (A) e + x?y? + cos 2y = c (B) e +…

A: To find The solution of the given differential equation.

Q: If (1 – i) x + (1 + i) y = 1 - 3i, then (x, y) =

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Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA…

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Q: 8 cos (t) – 1 for all solutions 0 < t < 27

A: The objective is to solve 8cos2t=8cos2t-1 for all the solutions 0≤t≤2π Consider, 8cos2t=8cos2t-1…

Q: The solution of (e + 2xy?) dx + (2 cos 2y + 2x y) dy is given by (A) e +x'y² + cos 2y = c (B) e"…

A: Given D.E is (ex + 2xy2) dx + (2cos 2y+2x2y) dy = 0     To find the solution of the given D.E .

Q: Consider the equation ut = Uxx, 0 0. Suppose u(0, t) = 0, u(1, t) = 0. Suppose u(x, 0) = -3 sin(x) +…

A: The given equation is  ut=uxx ,0&lt;x&lt;1,t&gt;0. Boundary Condition: u(0,t)=u(1,t)=0. Also…

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

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Q: The equation ? + sin(xy) + C = 0 is the general solution of O y' + cos (xy) = 2 (x + y) 2 (ydx +…

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Q: This answer is incorrect, could you please attempt it again?

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Q: Solve the he o-3D+4)y(x) =x cos(2x) equation y,(x)=(6x+4)sin( *+4)sin(2)-cos(23) - y,(x) =(-6x-4)…

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Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA.…

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Q: Verify that (e* sin y-2ysin x)+(e* cos y+2 cos x)y' 0is exact. Then solve it and leave the answer in…

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Q: Cos(x) 一+Sin (x) sec (x} I +sin (x) Cos(x)

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Q: f(x) = 2) f(x) = 1+2 cos 2x, 3) f(x) = 1-2 cos x %3D 2

A: (1)   Let the function be,   f(x)=x-1x   Find the domain of the functionf(x)=x-1x Here, the function…

Q: Find the solution of with y(0) 3 and y' (0) = 8. y = y" + 3y = 108 sin(3t) + 36 cos(3t)

A: see below the answer and explanation

Q: The solution to the IVP, is x₁ = 13x1 x2, x1(0) = x2 = 34x1+7x2, x2(0) = -1 x1(t) = e10t (cos(5t) +3…

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Q: s to find a particular sy1, y2 of the s(x))y'+(sin(x) - cos(x)) y = e 2 = e-* cos(x)

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Q: Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the…

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Q: Solve the general solution y4 + 2y" + y = x² sin x

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

A: We have to solve the system of equations.

Q: Find solutions using Exact Equations 1. Solve (y sin x + xycos x) dx + (x sin x + 1)dy = 0 2. Solve…

A: As per guideline , we can solve only one question at a time. If you want another question to be…

Q: sin(6x) cos(4x)dx% = %3D (b) ÷( + ) Nin (6x) cos (2x) COR +c 2. 2)+ (e) None Cos (2x) Cos (10x sin…

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