1. Solve the first-order linear differential equations. a) x+2y= 1-1, x > 0 x

Q: (Pe2y – x)dx = 2e²Y(e²y + Px)dy

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Q: 5) y=cixl+c2x+c3xlnx +4x? x'y"'+2x'y"-xy'+y=12x=

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Q: 4. y" + y = cos x when x = 0, y = 0, y' = 1 %3D

A: Given that:

Q: 3- Solve the differential equation (b and a are variables) (D²+4D+3)b=1+2a+3a?

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Q: Mickey Rats claim that y = xy - 5y is a separable and linear differential equation. Is he correct?…

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Q: (y² + 2xy)dx + x²dy = 0 2.

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Q: Solve the differential equation using Reduction of Order (D2 + 2D + 1)y = (e* - 1)-2 a. What is the…

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Q: (x + 1) + y = lnx, y(1) = 10 dy dx

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Q: yi = 3y, + 2y; y - +2y;

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Q: 4.Determine if the given function is a solution of the given differential equation

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Q: 2. Solve the differential equation y" + 3y csc V3x

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Q: ºu 20ºu 0x2 02 subject to the initial conditions u(x,0) = n(x), = F(x, t) du(x,0) dt v(x)

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Q: dI + 501 = 5; where I(0) = 0. dt

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Q: Solve the differential equation. (Assume the independent variable is x.) y" + 3y = 0

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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: dy 2 dx y+2 x+y- 1

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Q: The complementary function(C.F.) of the differential equation(D- 4) y = cos 4r is O (Ci +c21+ czz2)e…

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Q: 2) y = c1e5x + cze²2×.-ex : y"-3y'-10y=6ex 2

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Q: Determine the solution of the differential equation.

A: Answer and explanation is given below..

Q: Given D.E. Answer dy + 2xy² = 0 dx %3D

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Q: whether

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Q: y' + (1+ 2x2) .e²²+y = 0

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Q: I (1-x) y"- 4xy't 5x = cos x 2 d + tx=0 3. to ylm) _ t° y" +6y = 0 4. x + Y =0 dx 5. x y' - 4 seny =…

A: Linear equation means independent variable is in linear. That is independent variable is free from…

Q: 4. (2x – 5y + 1) dx – (5y – 2y) dy = 0

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Q: Find the linear differential equation that is satisfied by y=xe-xsin3x+2e-xcos3x.

A: Let's find linear differential equation.