Determine whether the equation (3x + 2y)dx + (2x + y)dy = 0 is exact. Find the solution if it is exact.

Q: Application3: A particle with mass m moves in conservative force field. Find the following in the…

A: Given: Mass of the particle =m Cylindrical coordinates are,  x=ρ cosϕ y=ρ sinϕ z=z.

Q: 2. (s-s?-t)ds + (t + s² +t ²)dt = 0

A:

Q: S2 cos (w - Sec W tan (w) dw

A:

Q: How do you solve this using differential equations?

A: Given: The detective got a call at ten past midnight. He arrived at the crime scene in 20 minutes.…

Q: Edisk = 1 4περ 2πστ Ꭱ r (r² + 22) 3/2 dr.

A: Edisk=14π∈02πσz∫0Rrr2+z232dr

Q: . By applying the method of undetermined coefficients, find the general solution of the following…

A:

Q: (e"siny + tany)dx + (e*cosy + xsec*y)dy = 0

A:

Q: 1. By applying the method of undetermined coefficients, find the general solution of the following…

A:

Q: 4x²yy' 3x(3y2 + 2) + 2(3y +2)3 %3D

A: Given differential equation is 4x2yy'=3x(3y2+2)+2(3y2+2)3 where y'=dydx We have to find the solution…

Q: 3. my²dx + m?ydy = 0

A: The simplification of the given equation helps to find the solution of the equation. Simplify the…

Q: 3. xy dx + x²ydy = 0

A: Given- xy2dx+x2ydy=0 To Solve- The above differential equation.

Q: 2. y" + 25y = 5 tan² (5x) cos(5x)

A: The given problem is to solve the given differential equation, we have to solve it by using…

Q: Consider the set U = {f € Co (R)| limx→∞ f(x) = 0}. That is, U is the set of all continuous…

A:

Q: (음 +) ( m)-" dy +2x d.r +2ry) 2e %3D dr

A:

Q: y" + y = secx tan x

A:

Q: dx = x- y + 1 dt dy = y - x + 2 dt

A: Given: dxdt=x-y+1                       1dydt=y-x+2                       2 The above system of…

Q: du х — у— 1

A:

Q: dy xy' = 6y + 12x*ys, (y' = dx

A:

Q: 5x

A: Integrate     4  dx/ ( 1+√5x)

Q: Find the solution of the initial-value problem dy 2y = 2x, y(2) = 8. dx

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Q: бу" - 7у - 5у %3D2x3 + е-* - 5

A:

Q: A tank initially contains 100 gal of brine whose salt concentration is lb/gal. Brine whose salt…

A: Given that The initial volume of brine in the tank = 100 gal The initial salt concentration of brine…

Q: g'(x) = 21x², g(0) = -2 g(x) =

A: Given: g'(x) =21x2  and g(0)= -2

Q: 1) (xy +y-x)dx + x(xy+ 1)0

A: A differential equation of the form M dx+N dy=0 It is said to be an exact differential equation if…

Q: 8. dy + ()y y dx = x* dx; y(0) = 2 2Vx. %3D

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.