Suppose that the characteristic equation for a differential equation is (r−3)^2(r−5)^2=0(a) Find such a differential equation, assuming it is homogeneous and has constant coefficients. Enter your answer using y,y′,y′′,y′′′,y′′′′ for the dependent variable and its derivatives.  (b) Find the general solution to this differential equation. In your answer, use c1,c2,c3c and c4 to denote arbitrary constants, use y for the dependent variable, and use x for the independent variable. Enter c1 as c1, c2 as c2, etc.

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: Solve the differential equation by using an integrating factor:y/+9y = x³e-9x Oxe-9 + C x²4e-9x +…

A: The given problem is to solve the given differential equation by using integrating factor. Given…

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.