dy The CF of the differential equation 3- dt? +27y = 0 is +18- dt a) CF =e*(c,x+c,) b) CF = e* (c,t+c2) c) CF = e"(c,t+c) d) y = e** O d) O a) O b)

Q: 3. Consider the second order differential equation _dx +7. + 6x = 0. dt2 dt (a) Convert the equation…

A: Given is the second order homogeneous second order differential equation: x''+7x'+6x=0 let us first…

Q: Verify that 1 $(x, y, z) = satis fies the partial differential equation x² + y² +z? = 0 ax2 ay2 "…

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Q: The standard form of the first order linear differential equation x'y'+ry +2=0is

A: The standard form of a first-order linear differential equation is:

Q: 1. Consider the system of differential equations: dy %3D dt dt Find a conserved quantity for this…

A: x°=dxdt=-yx2 y°=dydt=x+1 A conservative quantity H(x,y) requires that H(x,y) is constant on the…

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A: Given differential equation is u''−5u'+5u=e4t......1 We have to write the given differential…

Q: dr The differential equation dt2 -)² + sin() +1= 0 has degree dt dt (a) 3 (b) 2 (c) 1 (d) not…

A: We’ll answer the first question. Please submit a new question specifying the one you’d like…

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Q: Consider as following ordinary differential equations dy - 2y + 3y and dt dy = e" – 1. dt %3D…

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Q: Show that the set of solutions of a second-order linear homogeneous differential equation is…

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Q: Form the partial differential equation by elimaniting the constants form z=axey+1/2 a2e2y+b

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Q: The order and degree of the partial differential equation respectively 6 9. dz + sin x = xy? is_ %3D

A: Given,          ∂4z∂x46+∂z∂x9+sinx=xy2

Q: A mass-spring system is modelled by the differential equation u" + 16 u = 0 , and the motion starts…

A: Given that u''+16u=0   with   u0=7   and  u'0=4. Its auxiliary equation is m2+16=0. Solve as…

Q: Show that the partial differential equation has the general solution u(x, y) = e"[fx)+ g(y) where…

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Q: A solution to the partial differential equation. 9. is dy?

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Q: A mass-spring system is modelled by the differential equation u' + 16 u = 0, and the motion starts…

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Q: 3.) Let set S = {x, e*, sin x, cos x} be a solution to a 4th-order homogeneous differential…

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Q: 3.) Let set S = {x, e*,sin x , cos x} be a solution to a 4th-order homogeneous differential…

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Q: Form the partial differential equation by eliminating the arbitrary function z =x+y+f(xy)

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Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A: Here we find the first order differential equation of given function.

Q: What is the differential equation of the orthogonal trajectories of x3 = Cy? (1) Зxdx + 2уdy — 0 (2)…

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Q: State the order of the partial differential equation uxx + Uy = u + 4. Then classify whether it is…

A: We are given the following partial differential equations uxx+uy=u+4. The order of the PDE is 2.…

Q: The roots of an auxiliary cubic equation are m1=-1 and m2=m3=-5. What is the corresponding…

A: We have given the roots of an auxiliary cubic equation ,  m1 = -1  , m2 = m3 = -5 Thus , Auxiliary…

Q: 9. The characteristics of the partial differential equation *3 = 0 ду a əx dy +2- дх ду + cos? when…

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Q: Obtain the differential equation of all straight lines at a fixed distance p from the origin * O…

A: The general form of equation of a line which is at a constant distance c from the origin is…

Q: The motion of the mass-spring system is governed by the differential equation d²y dt2 dy + 6 dt + 9y…

A: The motion of the mass-spring system is given by the differential equation: d2ydt2+6dydt+9y=cos(2t)…

Q: Suppose that every constant multiple of a solution is also a solution for a first-order differential…

A: It is given that the differential equation dydt=ft,y, where ft,y is continuous on ty plane. Suppose…

Q: Let us consider a continuous-time system represented by the following differential equation : 5+ 3a…

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Q: Which of the following systems is equivalent to the differential equation y" + 9y" = cos(x) – y? 9uz…

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Q: Determine whether the given first-order differential equation is linear in the indicated dependent…

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Q: Which is the particular solution of the differential equation y"+ p(z)y'+ q(z)y=-2z which has two…

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Q: - Show that the partial differential equation = 0 has the general solution u(x, y) = e"[f(x) + g(y)]…

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Q: State the order of the partial differential equation uxx + uy = u + 4. Then classify whether it is…

A: The order of the highest derivative term in the equation is called the order of the PDE.

Q: If the auxiliary equation associated with a homogeneous linear differential equation with constant…

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Q: from the partial differential equation by eliminating the arbitrary function z (x² + y? + z?)

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Q: Find a homogeneous Euler-Cauchy differential equation whose general solution is Cx1+ C2x? where C,…

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Q: What is the auxiliary equation associated with the second order linear differential equation d^2x…

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Q: Utt - c?uxx = 0, – %3D

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Q: The order and degree of the partial differential equation respectively 6 9. dz + sin x xy is ду О…

A: Consider the given partial differential equation. Order of the partial differential equation is the…

Q: What is the differential equation of the orthogonal trajectories of x3 = Cy?? (1) 3xdx + 2ydy = 0…

A: Given x3 = Cy2

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Q: The formation of the partial differential equation by eliminating arbitrary function of z = 5f(x" –…

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Q: Solve the system of ordinary differential equations defined by dx/dt+y = cost dy/dt+x = −sint

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Q: What is the auxiliary equation associated with the second order linear differential equationd^2x…

A: We need to find auxiliary equation.

Q: Suppose g: IR →R has 3 distinct roots. How many distinct piecewise-constant solutions does the…

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Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

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Q: Find the function ?(?) that satisfies the differential equation dy/dt - 2ty = -6t2et^2 and the…

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Q: Form a differential equation from y =c(x' +2), here c is arbitrary constant. %3D а. dy (x² + 2) –…

A: y = c(x3 + 2)    ..............................(1) differentiation w. r. to x dydx = c3x2 + 0dydx =…

Q: Which one is the fourth order differential equation whose solutions are  e^(3x),e^(−3x) and  xe^(2x)…

A: We will use basic of ode.

Q: Verify that the indicated pair of functions is a solution of the given system of differential…

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Q: The order and degree of the partial differential equation respectively 8 9 az + tan x = x + y° ду is…

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