Find an integral formula for the general solution y(t) of the differential equation y''' − 6y'' + 11y' − 6y = g(t), t ∈ R, i.e., determine a function K : R × R → R of two variables such that y(t) = (integral from t0 to t)K(t, s) g(s) ds, where t0 ∈ R is a prescribed real number. Hint — The associated characteristic equation has the roots r1 = 1, r2 = 2, r3 = 3.

Q: The relative displacement u(t) of a single-storey shear building subjected to an earthquake ground…

A:

Q: Consider the differential equation rye) – Gry + 12y = 0. Show that the set { is linearly…

A: Given: x3y3-6xy'+12y=0 To find: xiri=1n is linearly independent.

Q: Show that the substitution v D ln y transforms the differential equation dy/dx+P(x)y=Q(x)(y ln…

A:

Q: Find the solution r(t) of the differential equation with the given initial condition: r' (t) = (sin…

A:

Q: Find a linear operating point model of the differential equation: d²x dx + 3 + 2x = sin x dt2 dt a)…

A: Consider the provided question, Given D.E, d2xdt2+3dxdt+2x=sinx We need to find a linear operating…

Q: Show that w(t) =〈sin(3t + 4),sin(3t − 2)〉, cos 3t satisfies the differential equation w''(t) =…

A: Given- wt=<sin3t+4,sin3t-2>,cos3t To prove- That the above expression satisfies the…

Q: -6 Verify that dz= xdx You ydy for x² > y² is an exact differential and evaluate z-f(x, y) from A…

A:

Q: Q1) Solve the following partial differential equation Ux + Uy = (cos x + sin y). U

A: 0

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.