Show that ¢(x) = Ce³* + 1 is a solution to dy/dx – 3y = -3 for any choice of the constant C. Thus, Cex + 1 is a one-parameter family of solutions to the differential equation. Graph several of the solution curves using the same coordinate axes.

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A: Solution of the given differntial equation is

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A: The given differential equation is: y'-8x3y=e2x4;       y(0)=2

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Q: A solution for the differential equation is y = Pe-3x/2 + Qe-x/2.

A: Here P and Q are two Arbitary constant ,so the heighest order of the differential equation is 2.

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Q: What will be the order of the differential equation if its solution is y=Acos7x-Bsin7x a. None of…

A: Homogeneous Linear Differential Equation with Constant Coefficients: A homogeneous linear…

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Q: Find the solution of the differential equation that satisfies the given initial condition. dy xp…

A: see 2nd step

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Q: Verify that the function y = Ce5x is a solution of the differential equation           y′ = 5y

A: The given function is  y = Ce5x  The differential equation is y′ = 5y

Q: (D – 3D + 2) y = (1+ e-")?

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

Q: y" + 25y = 5 tan²(5x) cos(5x)

A: To Determine :-  The second order differential equation : y'' + 25y = 5 tan2  5x cos  5x

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A: Given differential equation is, dydx=yx.

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Q: Find the indicated particular solution of the differential equation. dy dx + 7y= -2e - ⁹x; x = 0…

A: Topic = Differential equation

Q: If the general solution of a differential equation is y(t) = Ce-3t + 10, what is the solution that…

A: Given general solution of a differential equation is  y(t)=Ce-3t+10we have to find the solution that…

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