Non Homogeneous LDE solve: (D2  +  D  -  2)y  =  2x  -  40 cos 2x

Q: Q4) Solve the D.E = *-**y²+2x* ya dx

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Q: Solve: (3x – 2xy+ 3y)dx = 4rydy (y +3x)(y – x)3 = Ca³ %3D O (y + 3x) (y – x) = Ca³ (y – 3x)(y + x)3…

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Q: Solve, (2x+3y-2)dx+(3x-4y+1)dy = 0 %3D

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Q: Solve: (xy – 1) dx + (x² - xy) dy = 0 %D |

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Q: Solve (D5 – 2D4 + 4D³ – 8D²) y = 48e-2 16 sin (2x) - = A- B I = E E E P & O

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Q: B) Solve (3x? + 3x y²)dx + (3x²y – 3y² + 2y)dy = 0 %3D

A: First test for exactness:  ∂∂y3x2+3xy2=6xy ∂∂x3x2y-3y2+2y=6xy Since, ∂∂x3x2y-3y2+2y=∂∂y3x2+3xy2 so…

Q: xux-yuy+y2u=y2x find the general solution

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Q: dP/dt = P - P2 ; solve by seperation of variables.

A: It is required to solve the given differential equation using separation of variables. dPdt=P−P2

Q: Solve (D2+9)y=cos 3x

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Q: Solve (D² - 5D + 6) y = e sin x

A: Re-write the given differential equation as follows. D2-5D+6y=e sin xD2y-5Dy+6y=e sin xy"-5y'+6y=e…

Q: Solve 4y"+ 36 y = cosec 3x by using the method of variation of parameter.

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Q: Solve (D2+9)y=cos 3x

A: We have to solve the following differential equation: D2+9y=cos 3x   The corresponding homogeneous…

Q: b) Solve: (sinx+y)dx + (x + cos y)dy = 0

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Q: Solve RESISERE d³x dt3 +79²x dt² PERS + 6x = 0

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Q: Solve the solution: (D2 - D - 2)y= cos x

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Q: Solve (8) 2x2y′′+3xy′−y=0,x>0.

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Q: Q3) Solve x2ỹ –- 2xỹ + 2y = x

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Q: ydx+(2x+3y)dy=0 solve by using homogeneous equaations

A: We know,∫dxx=ln(x)   Given differential equation, ydx+(2x+3y)dy=0 ⇒dydx=-y2x+3y....(i)

Q: Solve by MUC: (D³ – D² + 3D + 5)y = e* cos 2x |

A: The given differential equation is (D3-D2+3D+5)y=excos2x Auxiliary equation is m3-m2+3m+5=0…

Q: Solve: (D - 2)²y 8(e2x + sin2x + x2

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Q: Solve (O+4D)(D-20)Z= Cos (2x) %3D

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Q: (D2+9)y=cos 3x

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Q: Solve (mz-ny)p+(nx-lz)q=ly-mx

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Q: Solve 2√√dy = cos² y, y(4) = . Use MATHEMATICA to plot the IVP solution. dr

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Q: Solve for GS: (D⁴+5D+4)y = cos (3x+4)

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Q: Solve exactly for ( 0, 2π)

A: Simplifying the given equation:Using the zero product rule:

Q: Solve (D? – 3D + 2) y cos (e-)

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