Find the particular solution to the following differential equation using the method of variation of parameters: y" + 6y+ 9y = t^2 e ^-3t

Q: Determine the solution of the differential equation: (3tanx - 2cosy)sec²x dx + tan xsin y dy = 0

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Q: Find a general solution to the given differential equation. Use the variation of parameters method.…

A: Given differential equation is y''+9y=sec2(3t). We will first find the general solution of the…

Q: Find a differential equation whose general solution is y = cet + c₂e-4² = 0

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Q: Use the varnation of parameters method to solve the differential equation 1. y"-y =

A: The detailed solution is given below Thank you

Q: Find the differential equation given the general solution: y = cer + Czex + 3x

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Q: Find the general solution of the differential equation: y' – 3y = xy. Use lower case c for the…

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Q: Form the differential equation of family of lines situated at a constant distance p from the origin.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Solve the differential equation by variation of parameteres: 4y'' - y = ex/2  +7

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Q: Find the differential equation which has y= asinx+bcosx+xcosx

A: Given: y=asinx+bcosx+xcosx                                   ..1 for finding differential equation…

Q: Find the differential equation by eliminating the arbitrary constants of the family of curves y = C₁…

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Q: Use variation of parameters to solve the differential equation x²y" + 10xy' + 8y = x².

A: The given problem is to solve the given differential equation by using the method of variation of…

Q: Solve the following differential equation: (y^2cosx-3x^2y-2x)dx+(2ysinx-x^3+Iny)dy=0

A: Given  The general solution is

Q: se variation of parameters to solve the given differential equation y" + y = tan:

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Q: Find the differential equations having as solution of y = x sin(xtc) .

A: We find the differential equations having as solution of y = x sin(xtc) .

Q: Use variation of parameters to solve the differential equation: -2x y" + 4y' + 4y : In x. = e

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

Q: Use the method of variation of parameters to solve the differential equation d'y dz² +9y = cosec²…

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Q: Find the general solution of the differential equation: y' – 5y = xy. - Use lower case c for the…

A: The given differential equation is y'-5y=xy2 This can  be written as dydx-5y=xy2 Divide both the…

Q: ta constant distance p from the origin. find the equation of the circle which touches both the axes…

A: All such lines are tangent to the circles of radius p                y=mx+p1+m2⟹   m=dydxBy…