Write the given second order equation as its equivalent system of first order equations. u" – 7.5u' + 1.5u = -3 sin(3t), u(1) = 0, u'(1) = = 1.5 Use v to represent the "velocity function", i.e. v = u'(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) Now write the system using matrices: :三一 u dt V and the initial value for the vector valued function is: v(1)

Q: Express the ODE æ''+x = tan(t) as a system of first order differential equations: r' = y y' = Now…

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Q: The characteristic equation for a 5th​ degree, homogeneous, constant coefficient DE is​…

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Q: Match the differential equation with its direction field. y' = 9(x + y) - 1 15 0.1+ -4.31 -0.2 -Q.1…

A: Matching the differential equation with its direction field  y'=9(x+y)-1 x 0 0 0 0 0.1 0.2 0…

Q: List the six orders in which the three differentials dx, dy, and dz may be written.

A: First type= (dx)(dy)(dz) Second type=(dx)(dz)(dy) Third type=(dy)(dx)(dz)

Q: Consider the system of differential equations: dx 2x – Y dt dy 5x – 2y dt Plot a well-labeled phase…

A: Consider a given system of ordinary differential equation: dxdt=2x-ydydt=5x-2y Plot a well-labelled…

Q: When a mass of 4 kilograms is attached to a spring whose constant is 64 N/m, it comes to rest in the…

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Q: Transform the given differential equation into an equivalent system of first-order differential…

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Q: When a mass of 4 kilograms is attached to a spring whose constant is 64 N/m, it comes to rest in the…

A: Solution :-

Q: 1. y' = xy ; xydx – dy = 0 %3D - %3D

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Q: The order and degree of the partial differential equation respectively 26 z 7 dz () + x = y? is, dy…

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Q: When a mass of 2 kilogram is attached to a spring whose constant is 32 n/m, it comes to rest in the…

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Q: Use the elimination method to find a general solution for the given linear system, where…

A: The given differential equation can be written as:dxdt=4x−2y+sint⇒D−4x+2y=sint​…

Q: Q3 Given a non-homogeneous system of the first crder linear differential equation as shown below.…

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Q: Write the homogeneous part of the differential equation system, namely f(x)= g(x)=0 in the normal…

A: u' (n) + v' (n) -2u (n) - v (n) -1/n =0 -2u'(n) -v'(n) + u (n) -v(n) x2 - 3n +1 =0 ddx-2 u + ddx-1…

Q: 4. Find the 6th order homogeneous linear equation whose general solution is: y = C1 cos t + C2 sin t…

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Q: Let the system of differential equations be given by dx = xy – x2 + 2x dt dy 2(y – 2Y, %3D - dt 2…

A: Let the system of diffrential equations be given by:-dydx=xy-x2+2xdydx=2y-xy2where x and y represent…

Q: Solve the system of linear equations for x and y.(cos θ)x + (sin θ)y = 1 (−sin θ)x + (cos θ)y = 1

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Q: Convert the differential equatim mto e System and Solle he System

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Q: Consider the following nonlinear equations. fi = sin(6x,)+cos(4x,)–1.5x, =0 f2 = e* +6x, +4x, = 0 f3…

A: To solve a system of three nonlinear equations with three unknowns, use the modified Newton Raphson…

Q: transform the equation into a systems of first-order equation: 2y(4) - et y' + 2ty = cos(t) y(0) =…

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Q: Solve of the following system of differential equations: (z' = 2x + y, %3D ¤(0) = 0, y(0) = 1. (y' =…

A: Given system of differential equations is x'=2x+y and y'=-14x+y with the initial conditions x0=0 and…

Q: Let the system of differential equations be given by dx = xy – x2 + 2x dt dy xY 2(y – ) dt where x…

A: For the system, dxdt=ax+bxydydt=cx+dxy If b>0,d>0 then the system is cooperative. If…

Q: Fiven the following non-homogeneous system of first-order linear differential quation: у3 2у1 + уг +…

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Q: Use the elimination method to find a general solution for the given linear system, where…

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Q: 1. y' = xy ; ; xydx – dy = 0 II

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Q: When a mass of 3 kilograms is attached to a spring whose constant is 48 N/m, it comes to rest in the…

A: we have to find equation of motion .

Q: Solve the system of differential equations x' 9x – 4y y' = 33x + 14y x(0) = 11, y(0) = – 30 = (?)x…

A: We will find out the required solution.

Q: Consider the vectors x1 (c) What conclusion can be drawn about the coefficients in the system of…

A: Given vector is, X1=t22tX2=etet Part(c): In case of linearly independent vectors X1 and X2. The co…

Q: Select the system of differential equations that is equivalent to the higher-order DE y" - 2y" +y…

A: Any higher order differential equation can be transformed into a system of differential equations…

Q: Assume that the number of immune cells is constant at density B0. The dynamics of the virus are then…

A: Consider the given equation. dMdt=rM1-MK-βMB0 (a) Where r is the reproduction rate virus. K is the…

Q: Find a root of the system of non- linear equations x +y = 3; xy 1 by Newton's method starting with…

A: here we need to find the root of given equation using newton's method. the solution is following.

Q: Match the differential equation with its direction field. y' = 10 - y \ 20 0:34 // 0.2f Q,1 -Q.31…

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Q: 2. Consider the system of differential equations: dr dy =1- y², = =(1+ y*) %3D dt Find a conserved…

A: An important trick to calculate a conserved quantity is to consider dydx corresponding  to the given…

Q: Consider the system of differential equations: dy dx = 1+y², - dt =x (2-y) dt Find a conserved…

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Q: Convert y" – 3t y'+3 y=cos(5 t) into a system of first-order equations.

A: The given differential equation is                                             y''-3ty'+3y=cos(5t)

Q: Assume that N(t) denotes the density of an insect species at time t and P(t) denotes the density of…

A: A prey-predator model describes the dynamics of the prey-predator population density at any time t…

Q: 38. Solve Find the system of curves satis fying the differential equating x2 1 a2 y² xdx + ydy + c…

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Q: convert the given linear differential equations to a first-order linear system. Q. y′′+ay′+by= F(t),…

A: Given differential equation is, y''+ay'+by=Ft      ...(1)

Q: cos X + cos t e' sin t, X' 1

A: Here is the solution of the given system of differential equations by using Method of Variation of…

Q: Consider the system of differential equations: dx 2x – Y dy 5x – – 2y dt Classify the equilibrium…

A: Find the Eigenvalues of the matrix corresponding to the system of linear equations. Since…

Q: Solve the following linear nonhomogeneous equation: y" (t) + 4y(t) = (sin 2t) 1. Hint: introducing a…

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Q: Sketch the slope field for the differential equation, and use the slope field to sketch the solution…

A: Slope field: A slope field is a graphical representation of the differential equation of the type…

Q: x' = -2x +y x(0) = -2 y(0) = 2 %3D y' = -5x + 4y %3D

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Q: Use the elimination method to find a general solution for the given linear system, where…

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Q: Recast the system of higher order differential equations as a first order system. u""=2u-3v…

A: The given higher order differential equations are: u'''=2u-3vv''=3tu'v'-cos u Recast the system as a…

Q: The standard equation of one dimensional heat equation is a'u ôu d'u ô'u d) a) b) a c) a?

A: One dimensional heat equation: Let u(x, t) denote the temperature at point x at time t. The equation…

Q: x(0) = -2 y(0) = 2 x' = 4x-5y %3D y' = x- 2y %3D

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Q: Solve the system of linear equations for x and y: (cos 0)x + (sin 0)y = 1 (-sin 0)x + (cos 0)y = 1

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Q: x' = -2x +y x(0) = -2 y(0) = 2 y' = -5x + 4y %3D

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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.