Consider the differential equation 4y" — 4y' + у 3D 0; еx/2, xeX/2. Verify that the functions e2 and xeX2 form a fundamental set of solutions of the differential equation on the interval (-0, ∞). The functions satisfy the differential equation and are linearly independent since W(ex/2, xe*/2) = + 0 for -o0 < x < ∞. Form the general solution. y =

Q: A ball is drawn randomly from a jar that contains 5 red balls, 7 white balls, and 4 yellow balls.…

A: From the given information, there are 5 red balls, 7 red balls and 4 yellow balls. The total number…

Q: (a). 2t²u" + 3tu'- u = 0,t> 0

A: The given differential equation is,let us substitute t=ez so z=logt and hence

Q: Given that y1 (x) = t* is a known solution of the linear differential equation ²y" – 7ty + 16y = 0,…

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Q: Consider the differential equation y" - y' – 12y = 0. Verify that the functions e3x e4x form a…

A:

Q: 3.- Show the differential equation is exact, then solve the equation. dy _ 3x2 - 6ху Зx? — у dx

A: To show that the differential equation is exact and to find the general solution

Q: Differentiate. Y(u) = (u-2 + u-3)(u5 - 6u²) Y'(u) = %3D

A:

Q: Solve each differential equations by integrating factors or reducing equations in exercises.

A: We will find out the required general solution.

Q: у" — Зу" + Зу' — у %3D х — 4е* -

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

Q: Find the differential equation that has y = C1 + C2x as its general solution. a) Oxy" – 3y = 0 b) O…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.