(iї) Зx' — 6х %3Dsin2t x(0) = 1 (iv) у" + 6у' + 13у %3D 0 У (0) %3 3, у'(0) 3 7

Q: у" — бу' + 9у %3 t'e", y(0) 3D 2, У (0) 3D 17

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Q: d^2y/dx^2-6dy/dx+9y=3xe^-3x+3x^2-2

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Q: (xy^2+y)dx -xdy =0

A: Given: (xy2+y)dx-x dy=0

Q: Solve for y: (D^3 - 3D^2 + 3D - 1)y=0

A: The solution are next step is

Q: x' -x? dxp x* +2x2 +1

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Q: y" - 8y + 25y = 0; y(0) = 0, y'(0) = 3

A: y''-8y'+25y=0; y(0)=0, y'(0)=3 We have to solve it using Laplace transform.

Q: 2x'+4x-6-0

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Q: y = 5t2 - 2t + 4 -'(t) =

A: The given function is y=t25t2-2t+4. We have to find the derivative of the given function. The…

Q: Eliminate the arbitrary constants: y=c_1 e^x+c_2 e^2x+c_3 e^3x O A. yA"+3y^"-9y+3y=0 O B.…

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Q: ∫ln(7)0∫ln(7)0e^−(2x+5y)dydx

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Q: Differentiate.

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Q: Differentiate. y=/3x² – 4 -3x y' = 3x - 4 3x y' = (3x2 - 4)-1/2 3 (3x² – 4) /2 3x V3x2 – 4

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Q: If f'(x) = and f(0) = 2, then f(4)can be written in fully simpi %3D S(x)

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Q: 1. 5х2у" + 23ху' + 16.2у —D 0 2. х?у" + 0.7ху' — 0.1у %3D 0 3. х2у" — 0.7ху — 0.1у %3D0 |

A: Given

Q: (D^3-2D^2-5D+6)y=e^(3x)

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Q: Question 3.5: Calculate o dz. Question 3.6: Calculate o 1 - dz .

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Q: Find the y_(p ) of y^(')'-5y^(')-6y=18x^(2)+12e^(2x) 2

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Q: F"(x) = 6-18x, 0) = 9, 2) = 11 F(x) = 4x -3 +Ox+9 3p3 O Tyne h

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Q: find the solution (4D^2-4D+1)y=0 when x=0, y=-2, y'=2

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Q: The general solution for the equation y'=x*e(x^2+y) can be given in the form of: ?ex^2+2e-y=k a) x…

A: Solve by separable variable method

Q: Find dy/dx: a. 3x? – (xy²)/2 = 2y³ b. y = (cosx – nx)^**

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Q: e y" – 2y' + y = 1+ r² 2y' + у 3 + Зе* 1 + r2

A: Given,

Q: y^ (4) + y”” + y” = 0

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Q: Solve the equation (x^4 + 2y)dx - xdy = 0

A: I am attaching image so that you understand each and every step.

Q: y=(x^2+1)^4 y`(1)=?

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Q: Find the solution. (403+12D²+13D+10)y = 0. @ y=c,e+e>(c,cosx + c sinx) +c,sinx) -3x y =…

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Q: Which of the following equation is a variable separable DE? a. (x + x^2y) dy = (2x + xy^2) dx b. (x…

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Q: 4x2-5х+6, 3. S(*-*+*)d *“)dx x2

A: We have two types of integrals in general, namely definite and indefinite integrals . The definite…

Q: 5. (y" – y) = e-X cos(3x) %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (b) 를/ dx 3

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Q: (бх - Зу +2)dk - (2xх - у -1) dy 3D0 |

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Q: Y"+y=secxtanx

A: Given, y'' + y = secx tanx This is a second order linear, non-homogeneous ODE. We can write the…

Q: 1 = felan(4x*). sec²(4x²)xde 2

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Q: Find all solutions to the equation (D^2 − 3D + 2)y(x) = 2e^3x.

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