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

Q: 9. Solve d²x dt² + 4x + 5y = 1²; d²y dt² + 5x + 4y = t +1.

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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: equilibrium

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Q: x2y3-y=x+x2 find dy/dt

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Q: Solve system of linear DEs  dx/dt+dy/dt+2y+6y=2e^t 2dx/dt+3dy/dt+3x+8y=-1

A: To solve dxdt+dydt+2x+6y=2et2dxdt+3dydt+3x+8y=-1

Q: d/dt (t2 + 1/t + 1)

A: Given ddtt2+1t+1

Q: find dy/dt.

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Q: et d Calculate dt \e +1) ()

A: The differentiation is a process of finding the rate of change of one variable with respect to…

Q: What is the characteristic equation of d^2y/dt^2 -7dy/dt +10y = u? d²y dy -7 dt² dt + 10y = = U

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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: 1. 2d2y/dx2 - dy/dx + y = 0 2. d2x/dt2 + 4dx/dt + 4x = 0 3. 2d2y/dx2 -3 dy/dx +2y=0

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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: ctan x (2) Let h(x) = t dt, calculate h'(T/3). ww. t2 + 2

A: Solve the following

Q: 2. で-5e dt = 4.

A: ∫xndx = xn+1n+1

Q: 6. S t √1+2t dt

A: The given integral,    ∫t1+2t4dt

Q: () Find the solution that satisfies Y(0) 1

A: We will find out the required solution.

Q: Jse variation of parameters to find a solution o the given system: dx/dt%3D2Y+2…

A: Given system isdxdt = 2y+2 ; dydt = -x+3y+e-3t ; can be reduced asx'y' = 02-13xy+2e-3tis of the form…

Q: + y = ty dt

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Q: Draw the bifurcation diagram for dy/dt = y(a-y)

A: We can use concept of critical points in order to solve the given problem.

Q: f(2) 1 dt, then f'(z) = ++1

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Q: What is general solution of v = ds/dt if v = 2/t^3/2? a.-4/t^1/2 = s^2 + c b.-4/t^1/2 = s + c^2…

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Q: is A+Ce^(-kt) a general or particular solution to the DE dT/dt=k(A-T)

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Q: - choose the correct answer If y = t^2/(t^2+1) and t= v(2x+1) the = dyldx %3D 1/N(2x+1) O 2(x+1)^2 O…

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Q: 1 So 2t en + e-2t ezt - e-at dt

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

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Q: Find dX/dt of Matrix:

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Q: S t /1+3t - dt

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Q: Use the separation of variables to find the general solution to dy/dt = (3t + 2)*y^(4) Be sure to…

A: We have to find the general solution to the differential equationdydt=(3t+2).y4

Q: t2+1 = 0 dv Vt- dt V+1

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Q: Find the annihilator:  f(x) = cos(2x) +4sin (3x)  a. (D^2 +3)^2  b. (D^2 +9)(D^2 +4) c. D^2 - 4D…

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Q: Determine whether the given equation is separable, linear, neither or both.  (t^2+1)dy/dt=yt-y

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Q: Find dy/dx

A: Here we use fundamental theorem of calculus, in which to find the derivative of a definite integral…

Q: xy5 = zy"+yx²

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