2. Show that cos(wt – B), coswt, sinwt are linearly dependent functions of t. Show Complete Solution

Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: FIND 2 DIFFERENT (LINEARLY IN DE PENDËNT ) SOLUTION S POR THE D.E y"_x² y'- 3 xy = O *y'-3xy%3D0

A: Step:-1 Given that y''-x2y'-3xy=0 ---(1) This is second order differential equation with variable…

Q: dw Use the Chain Rule to find where w = cos 8x sin 2y, x = and y = t*. dt 4' dw II

A: w=cos8x sin2y  , x=t4 and y=t4 dxdt=dt4dt=14 dydt=dt4dt=4t3   ∂w∂x=8 cos8x cos2y ∂w∂y=sin8x -2 sin2y…

Q: [3] Consider the equation for free mechanical vibration, my" + by' + ky = 0 and assume the motion is…

A: Given equation is, my''+by'+ky=0 So, the auxiliary equation of the given equation is,…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 4 cos x – sin xy; y = 7t || Enter the…

A: We have to find

Q: Solve the following problems by applying chain rule. dw (a) If w=x -2y² +z', and x= sint , y=e', z=…

A: We have to applying chain rule and solve given problem

Q: The function is given in parametric form by the equations{x=t2+t−1y=t3−2t.Find the second-order…

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Q: Find a particular solution of the equation y2y' = cosx satisfying the initial condition y(0) = 0.…

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Q: show that the solution y(t)=e^2t(cos(t)-2sin(t)) is linearly independant.

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Q: EXERCISE 1. dy ry+y Find the general solution of dr

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Q: Compute the solution of the IVP Sz(t) = (sin f)z(t) + sin t, l-(4) = 1, using the method for linear…

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Q: dw Use an appropriate form of the chain rule to find dt 1 y = t, z = to w = 3 cos xy – sin xz3; t'…

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Q: Show that f(x, y) = ln(x2 + y2) solves Laplace's equation, ∂2z ∂x2  +  ∂2z ∂y2  =…

A: Given Laplace’s equation is

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: Solve the following system of equations using ode45. dy = -4y, – 2y2 + cos(t) + 4 sin(t), y,(0) = 0…

A: We will solve this problem using MATLAB with ode45. The code and corresponding solution curves are…

Q: Use the SlopeField command in GeoGebra to obtain a direction field for the differential equation dy…

A: Here we have to draw the slope field for the given differential equation and then the plot the…

Q: Determine whether the functions y, and y, are linearly dependent on the interval (0,1). y =sint cos…

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Q: Find the general solution of the Euler equation on (0, oo) x²y" 3xy' + 13y = 0 y(z) = Note: Use A…

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Q: Find the solution for three cases of damped motion. my" + cy' + ky = 0 with m= 10, k = 90 y(0) =…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x y = 2t t' Enter…

A: This question is based on Derivative.

Q: The equation implicitly defines z as a function of t. Find dz dt 11 dt cos (3 z) = -8

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Q: Which of the following is not linear? a. 3. 2x + Vy? – Vz3 = 4 (sin T1/2)x1 + 4x2 = cos245 b.…

A: Which of the following is not linear? a 2x+y2-z33=4b sinπ2x1+4x2=cos245c 12x-y+πz=4d…

Q: Let z = x?y + 3xy+ where x = sin 2t and y dz find = cos t. Use the chain rule to when t = 0. dt

A: See solution below. Using definition of chain rule.

Q: whether the equations are linear or non-linear and homogeneous or inhomogeneous: (1) Ury + Uyyy –…

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Q: Find one particular solution to the following second-order forced equation d²y dy +8 + 15y = 5…

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Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

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Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

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Q: dw Use an appropriate form of the chain rule to find dt 1 w = 8 cos xy – sin cz; x = y=t, z = t7 t'…

A: Here we have to find dw/dt by chain rule.

Q: Show that the kinematic differential equations of the (2-3-2) Euler angles is 0 = [B(0)]» %3D where,…

A: Let us first find the kinematic differential equations of the (2-3-2).

Q: Find a linear differential operator that annihilate the given function a) y=7e2x b) y=x+3xe6x

A: We know that gD is annihilator of y if gDy=0 (a) y=7e2x Differentiating wrt x, Dy=7×2e2x, D=ddx is…

Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x sin ry; y = 9t t' Enter the answer…

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Q: Suppose w = 2x2 + 8y², Compute dw/dt in two different ways: x = 7 cos(t) + 5 sin(t) , and y = 7…

A: The chain rule is mentioned below: dwdt=∂w∂x·dxdt+∂w∂y·dydt

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 6 cos x – sin xy; Y = 8t %3D t' Enter…

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: 5.Express this model of an electric circuit d²y dt² dt As a pair of first order equation +6+5y=sin…

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Q: Consider the following simultaneous equations model. Assume that x is exogenous. yi = Bx + e Y2 =…

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Q: T/2 %3D cos (2wt + O, + ©z)dt = 0 -/2

A: The solution are next step is

Q: If C, and C, are constant vectors and A is a constant scalar, show that H - e* (C1 sin Ày +C2 cos…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x – sin xy; x = y = 2t t' Enter…

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Q: Suppose tôx1 + 2x2 + sec(t), %3D sin(t)x1 + tx2 – 3. This system of linear differential equations…

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Q: 5.Express this model of an electric circuit d²y dy +6 +5y = sin10t, y(0)=0, y'(0)=1 dt² dt As a pair…

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Q: Let y= a,+a,t+ azt? + a3t³ + a4t* + agt5 + agt6 +...... be the solution of d?y ад dy +t- +y=tan-'t ;…

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Q: Convert the following differential equati integral equations and draw direct form. direct form II…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Verify that y = x[cos (Inx)] is a solution of x²y" – xy' + 2y = 0

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Q: Find the general solutions to the following non-homogeneous Cauchy-Euler equation using variation of…

A: According to the given information it is required to solve the differential equation:

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos x :- sin ry; y = 9t Enter the…

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