If the general solution of the differential equatino system dx 2х — 5у dt dy 2у + x %3D dt x(t) = c,e3t + c,e=3E %3D is then what is the relations between C,C2 y(t) = cze³t +Cze=3t and c3, C, ?

Q: dy = 2y and the solution to this equation includes the point (-1, 1), then y = dx 5. , Given (A) e²r…

A: Given : dy/dx= 2y includes point (-1, 1)

Q: Q2: If D = d dt > find a complete solution of: (D+2)x+ (D+4)y = 1 (D+1)x+ (D+5)y = 2

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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: In this equation, y=15x. What is the constant of proportionality?

A: Constant of proportionality is K then y/x = k is relation y = 15x y/x = 15 so that k = 15 i.e.…

Q: (E) 18. Consider the function f = e2"y – xy tan 3x+7. Compute the gradient of f, and compute all…

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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: A form of a particular solution to = 2x + 3y-7 dt = -x - 2y +5 is dt O (a b)" O (7, 5)" O (2, y)" O…

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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

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Q: Find two linearly independent solutions of 2x²y" - xy' + (−3x + 1)y = 0, x > 0 = x¹¹ (1 + α₁x + a₂x²…

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Q: This problem is about the constant coefficient linear inhomogeneous equation p(d/dx)y = f(x) where…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

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

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

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Q: Suppose that a consumer derives his utility from two goods, the amounts of which are x and y,…

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Q: 10. Consider the linear regression model with assumptions (i) to (iii) and (iv*) with V = k? I, + V1…

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Q: Consider the equ dS = (1-P)r - BCS ty C - S dt dc = pcs dt. d I dt. • SCIR disease type model pcs -…

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Q: (Зху — 4у — 1)dx + x(x — 2)dy 3D 0; when x — 1,у %3D 2

A: According to  given Bartley guidelines to solve only one question at a time if it is not mentioned…

Q: 3 L[y] =y' --y is a linear operator. If u(x) = −4x² + 2x, then find L[u(x)]. X a) -4x² - 6x b) -…

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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: W = 0.3RX +0.7Ry, where Rx is the stock return from investing in stock X and Ry is the sto investing…

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Q: (c) Consider the double integral || xy dA where D is bounded by the x-axis and the upper half…

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Q: system

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Q: x = 2x - xy + (1/2)x²

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Q: b) y(4) + y(3) – 7y(2) – y' + 6y = 0. c) y(4) – y(3) – 7y(2) + y' + 6y = 0.

A: Solve the given differential equation Here I am giving answer of 1 st problem if you want answer of…

Q: One model for expenditures at high school gives the cosr C, in dollars per pupil, as a function of…

A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…

Q: There are only two companies that produce running shoes: X and Y. The shoes they produce are similar…

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Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

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Q: az Calcula y z = x4 – 2y3 O 8z 4x3 az -6y? O az 4x – 2y dz = 1* – 6y O dz = 4x3 az = 6y? O 8z 4x –…

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Q: Check if the system with the following input-output relation are i) Memory/memory less ii) Causal…

A: a) Here, the relation is, yt=x4t+xt-3.

Q: Find the general solution of the given ODE dy x + 2y - 3 2+y−3 = dx (x + y)² = C(x + y − 2) Option 1…

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Q: 5. Find the general solution of (x + y + 1) dx + (x – 3y - 7) dy = 0 %3D x? - 3y? + 2xy + 2x x? +…

A: To find the general solution of the given differential equation

Q: dy Solve the following implicit partial derivative dx and select the correct answer:…

A: sol is given below..

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

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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.