Consider the partial differential equation D 0°C V or? 1 ƏC Ox r ôr C=C,x=0 0,r = 0 - D- Or : KC,r=1 Or Apply the Laplace transformation and write the general form of the solution in the Laplace domain (do not try to invert).

Q: 1. Find equilibria, find the potential, classify the equilibria using the potential. Sketch the…

A:

Q: Write a in the form a = a-T+ anN at the given value of t without finding T and N. r(t) = (6 e'V5) i+…

A:

Q: dY 1 dt -1 a

A: This is a problem of stability Theory, a system of the differential equations.

Q: Use Laplace transformation to solve the initial value problem y' + 2y = u(t) sin (2t), y(0) = w,…

A:

Q: 1 dr r do = ²-1 r² +1 tan 0.

A:

Q: Q4:- Solve the following equation using Laplace transformation: y" + 7y= 10e²t,y(0) = 0, y'(0) = 3.

A:

Q: show that the function y = Ae- Is Eigenfunction for this operator d? 2 d + + dx2 'x dx 2a Where A…

A: The solution is given as

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.