y = Ceax cos(bx) + C2eax sin(bx); a and b are parameters

Q: 1. y = c1e-2x + cze²x + cze2x 2. y = c1e* + cze3x

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Q: x² y' - 2lnx - e2y+4(Inx)/x = 0

A: Given: The given differential equation is x2y'-2lnx-e2y+4lnxx=0

Q: dy - 2y + 6 Find the solution of the differential equation. - dx 2.x + y + 2 ||

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Q: Find a differential equation whose general solution is y = c₁e²t + C₂e-2.

A: Note: Your general solution should be: .The differential equation for this general solution needs to…

Q: y-3y+2y=2x +sin x+(1+2x)e" +4e* %3D

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Q: Determine the particular solution of the given differential equation: 6y' – 2y = xy* @ y(0) = -2

A: This differential equation is in the form of Bernaulli's equation. So first we reduce it in the…

Q: Determine the solution of the differential equation.

A: Answer and explanation is given below..

Q: d²y dy e* - 2 + 2y = dx² dx cos(x)

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Q: y' + (1+ 2x2) .e²²+y = 0

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Q: e"(dr+3rde)=0

A: To solve the given differential equations.  e3θ(dr + 3rdθ) = 0.

Q: 1.3x – xy = c -

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Q: b. y = C1e²*cos3x + Cze²*sin3x %3D

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Q: d²x dt² solve for x. 2 + w³²x = F sin wt

A: Given differential equation isd2X/dt2  + w2X = F0 sinwt

Q: (D² + 1) y = x cos x

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Q: * + 10x + 21x = 0 x(0) = 4 x(0) = -3

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Q: dp = t°p – p + t² – 1 dt %3D

A: A first order differential equation in separable form is given by: dydx=gx. hy & hy≠0 where gx…