0 < x < 1, t > 0 t > 0 0 < x < 1 0< ¤ < 1 Utt Uz(0, t) = uz(1, t) = 0 u(x, 0) = f(x) = 2 cos(3rx) + 4 u (x, 0) = g(x) = sin? (rx) – cos (rx) (Hint: use trig identity (double angle) to rewrite sin (Tx) – cos² (Tx) into cosine series 4. Solve the wave equation form.)

Q: Show that u(x, t) = 4 tan-1 I-ut ev where v is constant, is solution of Uxz – Utt = sin(u)

A: To check the given solution satisfy the given partial differential equation, substitute the solution…

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: (3e* sin(y) + y)dx + (2x + e* cos(y))dy = 0 not exact

A: Que is not clear though. We Shall check exactness for the given differential equation. If you have…

Q: 1 (d) NZ V2 2x sin-1(x² | 0.

A:

Q: as a function of x when y =

A:

Q: c) f(x)=tan(cos².x) 11 COS X 1+ sin.x Dy=- b) y = 2

A: e)  f(x)=tan(cos2x)  f) y=cosx/(1+sinx) g) y=ex^2/x3 Repost the next part.

Q: i. y" - 4y + 5y = 39xe* sin(x) + 47e * sin(x)

A:

Q: 2. (5) Find f, for the function f(x, y) = sin (x + y²)

A:

Q: secx + 1 51. secx - 1 (cscx + cotx)? %3D 52 56 verify that the equat

A:

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.