(a) (b) (c) d'y dy dx² dx dx² d'y dr.² -6y=0 dy -4+8y=0 dx +3 dy dx +2y=0

Q: A bacteria colony begins with a population of 120 and quadruples in size every 1.5 days.   If the…

A: Given initial population = 120  So, for t=0, P=120  Using that we get: Quadruples in size every 1.5…

Q: Find the general solution to the linear first-order differential equation: -+ dx 3x x²+1= 1 6x x²+1

A: The given differential equation,.The objective is to find the general solution to the differential…

Q: y = Ae* + Be-*

A:

Q: Consider the equation y' - 4y = tet State the integrating factor u(t) and find the general solution…

A:

Q: Consider the differential equation 4y" – 4y' – 8y = . Find a particular solution for the given…

A: Given differential equation 4y'' - 4y' - 8y = 8ex

Q: Solve the general solution of the second order linear differential equation with constant…

A: rewriting the equation we get  y'-1t2-1y2=-1t2-1

Q: = csc x – ycotx

A:

Q: (D – 3D + 2) y = (1+ e-")?

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

Q: Solve the ordinary differential equation 4xy" + 3y' +3y = 0. The %3D aelution with an integen…

A: Given: The differential equation is, 4 xy'' + 3 y' +3 y =0  .....(1) And integer x = 0.96

Q: Find a differential equation whose general solution is y = cje% + cze¯74. = 0

A:

Q: Given any first-order differential equation, outline a process for determining an appropriate…

A: We have to give the process for determining an appropriate solution method.

Q: 7. у"" + у" — 7у" — у' + бу %3D 0 - -

A: On solving this differential equation we will get

Q: Verify that the given function y = 5e¯* is a solution to the differential equation defined by. Do…

A: Explanation of the answer is as follows

Q: Write down a differential equation of the form = ay+b where all solutions approach y = dt as t → 0.

A: The given question is solved below.

Q: What is a Solution to an Ordinary Differential Equations?

A: The Solution to an Ordinary Differential Equation is an equation that satisfies the given…