Solve the S-L problem. y" + ay = 0 y(0) = y(1) & y' (0) = y'(1)

Q: Solve x*y"- 2x(1+x)y'+2(1+x)y= x'

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Q: Match the D.E. with a direction field: y' = t+y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2 –…

A: NOTE: Horizontal axis is t-axis  .

Q: y = (c1 + c2e2= + c3e¯® + C3e¯ cos(2x) + c4eª sin(2x))

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Q: Let y = Arcsec (cos² 3x). If y '= == A (B C) D) - 6 tan3x - 3 sin3x - 6 sin3x cos3x N 2 cos3x D and…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find y'' in y = x(2x + 1)4

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Q: Find the solution to the equation y' - y = x2y2

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Q: Solve y" + (y')² = 0.

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Q: y' + (=) y = xy²

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Q: Solve of the following Clairaut equation y=((x+4)y')+(y')^2

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Q: 2) Solve the equation y' = Y 4x²y + x

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Q: + ¹² = 4t, where y'(1) = 1 and y(1)=2. 4) Solve y" +

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Q: 2yy" = 1 + (y')² 2

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Q: y2(1+(y')2)=x+y'y find the general solution to the equation.

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Q: 4) Solve (xe + ye" )dx+(xe" +e' )dy = 0

A: The differential equation is xe-y+ye-ydx+xe-y+eydy=0 Write it as: e-yx+ydx+x+e2ydy=0x+ydx+x+e2ydy=0…

Q: Solve X'

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Q: 3x²y' = x(5-6y) x = 1; y = 2

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Q: Find y'

A: given

Q: 1. Find a general solution of the first order equation: y'= 3x²y².

A: The given first order differential equation is solved by method of separation of variable.

Q: INTEGRO-DIFFERENTIAL 1. y" + 5y' - 4y = 0

A: Given: y''+5y'-4y=0 y(0)=2y'(0)=4

Q: 5. Solve 2y" - 3y' - 2y = 0; y(0) = 1, y'(0) = -1.

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Q: 2. Solve y" + 2y' – 3y = 3, y(0) = y'(0) = 1. II %3D %3D

A: given differential equation is linear non homogeneous differential equation with constant…

Q: Qlevatuate the fottowing tAtegrats5

A: We need to find ∫11+cosecx dx, where x is the angle.  Now, cosec x=1sin x Therefore,  ∫11+cosecx…

Q: Solve the Bernoulli equation   y'-2.8y=-0.28y^2

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Q: Find y'. 9) y = (5x-2)(3x + 1)

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Q: y'=(2x+2y+1)/(x+y-1)  Solve the equation.?

A: Consider the given equation. y'=2x+2y+1x+y-1 Put v=x+y in the above function. dvdx=1+dydx

Q: Solve y’’ – y’ + y = 2sin(3x)

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Q: (1) Solve x'= 2. -36

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

Q: If y" = 6x + 2 and y'(1) = 2 and y(1) = 2, find y.

A: If y" = 6x + 2 and y'(1) = 2 and y(1) = 2, find y.