If the general solution of the differential equatino system dx 2x – 5y dt dy 2y + x dt x(t) = c,e +€ze at is y(t) = c,edt + Cze then what is the relations between €, Ez =3t and c3, C ? a)G =-5c,, Cg C4 b) e = 5c, , Cz ==C4 d) = C,, Cz =-5c4 e) G = -C3, C2 = 5c4

Q: Use the characteristics method to determine the solution for the equation d2y/dt2 + dy/dt +3y = 0.

A: Dear student we are write the ordinary differential equation so  we use the characteristic equation…

Q: A system of the type i = f(x), f(x) = -gradV(x), is called a gradient system. Investigate the…

A: Given that, A system of the type x˙=fx, fx=-grad Vx is called a gradient system.  Investigate the…

Q: fa(4, 3) = 2, fy(4, 3) = -6, 6. dz find at t = 2 when x = g(t), y = h(t) and dt g(2) = 4, g'(2) = 2.…

A:

Q: The system dx/dt = x + y, dy/dt = x + 2y + 1 has a constant solution. true or false?

A: dx/dt = x + y,dy/dt = x + 2y + 1

Q: 1. d²y dt2 dy + 6- +8y=2e-3t dt 2. d²y dy +4 dt² dt +13y = e-t 3. d²y dy +7 +10y=e-2t dt2 dt

A:

Q: 2. The behavior of the system is a saddle. x' = -x +y, y = -x-y

A: The given system of differential equations is:…

Q: ds/dt if s=(t9+6)(t8-6)

A:

Q: Let y= ao+ a1t+ azt + a3t³ + azt“ + ast° + agt°. d'y +...... be the solution of dy + t- dt ; y(0) =…

A:

Q: Find the equilibrium point. D(x) = 7- 8x, S(x) = 3 + 8x

A: Equilibrium point is the point at which demand and supply function intersects. That means at…

Q: Q4/ In a mass-spring-damper system, the acceleration x₁ (m/s²), velocity x₂ (m/s) and displacement…

A: We are to solve for x_1 , x_2, x_3

Q: Find all the second order partial derivatives of the given function. 10) f(x, y) = (x2 + y2)7

A:

Q: The function u depends on two independent variables: u= u(x, t). Find the general solution of the…

A: Given: The function u depends on two independent variables: u=u(x,t). PDE: ∂2u∂t2+∂u∂t+u=2t-x. To…

Q: True or False The system dx/dt = 2y dy/dt = sin(xy) has only one equilibrium point.

A: We need to equate both the derivative to 0, to calculate the equilibrium points.

Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

A:

Q: 4. Find the four second partial derivatives for f(x,y) = x²sin y. state final answers and show all…

A: NOTE: Refresh your page if you can't see any equations..Take the partial derivative with respect to…

Q: 4) Find all first-order partial derivatives w = f(x,y, z) = 2x³y³ – /xyz + 4z6x y3

A:

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: Suppose that fx = 3x + ay², fy = bxy + 2y, fy (1,1) = 3 and f has continuous mixed second partial…

A:

Q: find the general solution to dy/dt = {{3,-1},{4,7}}y

A:

Q: Which of these is NOT an eigenvector? 4 4 1.3 -1.

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.