dy (a) dt + 2y(t) = x?(t) dy (b) dt + 3ty(t) = tx(t) (c) 3y(t) +2 = x(t) dy (d) + y?(t) = x(t) dt (2) 2 dy +2y(t) = x(t) (e) dt dy dx (f) + (sin t)y(t) dt + 2x(t) %3D dt dy (g) dx +2y(t) = x(t)- dt

Q: Question 2 Let p be a prime number. Show that (p- 1)! = (p - 1) (p – 2) .2.1 = -1 holds in F, (Hint:…

A:

Q: (xy^2- y^2+x-1)dx + (x^2y-2xy + x ^2+2y-2x+2)dy = 0 Start by using seperable equations.

A: given a differential equation,here need to solve this differential equation by seperation of the…

Q: xy Find all second order derivatives for r(x,y)= 4x +9y

A: The given function is

Q: x+y y² +1 #2) (x + tany)dx +- -dy = 0.

A: here we have to solve the differential equation.

Q: (2t – 3)·e -t²+3t dt 3 2/Inx dx . X (2у-3)12

A:

Q: dy -: y = 6x² – 4x, dt dx = 7,x = -2 dt (5) Find -

A:

Q: 故(x3+5) ex A al d Iny d in5x

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Find dy dt O A. O B. O C. O D. 2 for y=(5t²-4t) ². dy dt dy dt dy dt dy dt = 2(10t-4) = 2 (5t² - 4t)…

A: Given: y=5t2-4t2We need to find dydt.

Q: (a) (b) (c) dy dt dy dt y (0) dy dt || - t sec(y) y (e¹²) 2t + sec²(t) 2y == 5 -t (y-1)² 3

A: Here, we have to solve given differential equations using method of separation of variables.

Q: Dy/dt = 2y(5-y) is the equation autonomous?

A: An autonomous equation is a differential equation in which the independent variable does not appear…

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.