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: find the a general solution to dy/dt = {{-9,12},{6,-8}}y

A: (.)  Given ,            (.)  Consider a system of differential equation ,…

Q: d²x_dx Verify that x = C,e¬t + C2e2t is a solution to dt2 2х — 0. - dt

A: To verify the given statement.

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: How do you integrate this: ∫(50+2t)3(10) dt + c c = is just an arbitrary constant

A: Indefinite Integration

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: Consider the nonhomogeneous linear equation y" +9y' g(t) with the complementary solution y,= c1y1(t)…

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: onsider the following equation system: (P =r – Q – I+w P= α + Q | I = BQ + Vw here Q,P,I are the…

A:

Q: Find f(1) if f(t) dt = x- x + 2x2- 2, x >1. %3D

A: Given, ∫1x2ftdt = x6 -x4  +2x2 -2               x≥1 We have to find   f1

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: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…

A:

Q: 4) Demand for a model of SUV is given by the formula: √x D(x, y) = 45,000 10 (5y - 11)3/2 where x is…

A: Demand for a model of SUV is given by the formula, D(x,y)=45000-x2-10(5y-11)32 We have to find the…

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: 12vt dt (1+t3/2)2

A:

Q: Find dX/dt of Matrix:

A:

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: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

A:

Q: Illustrate the numerical approximation of solutions of systems x' = f (t , x) ,    x(t0) =x0

A: We have to give an approximation method to solve given first order differential equation .

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: system

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: x = 2x - xy + (1/2)x²

A:

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

A:

Q: Given that the three-state model equation are d[A] dt d[B] dt d[C] dt -a[A] + B[B] = = a[A] -…

A: As per the question we are given a three-state linear dynamic system and the solution for the…

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: dx/dt = X +y dy/dt = 2x + 2y

A: To solve dxdt=x+ydydt=2x+2y

Q: Find all the second order partial derivatives of the given function. f(x,y) =xy? + ye * + 5 O A. 2f…

A: Given :  f(x, y) = xy2+y ex2+5 We have to find all the second order derivative of the given function…

Q: 5 +4y = 2 y(0)=1 dt

A: Given problem is:

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.