Use the Laplace transform to solve the given initial value problem (y' = dy dt Y(s) = y" + 6y' +9y=0 y(0) = -3, y'(0) = 11 (-11 - 3s) S +65 +9 y(t) = -3e -3t X + 17 te -3s - 7 s² + 6s +9 -3t

Q: consider the ODE y'=2y/x, y(x0)=y0 does it have a solutioon for i. x0=0 and y0/=0…

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Q: (a) Determine all critical points of the given system of equations. (b) Find the corresponding…

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Q: (D^3 + 2D^2 + 12D - 40)y=0 when x=0, y=0, y'=1, y''=0

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Q: 6. S t √1+2t dt

A: The given integral,    ∫t1+2t4dt

Q: solve the non-homogenous equation y” – 2y’ = t + e^t

A: The given equation is a non-homogeneous second order differential equation. The general solution of…

Q: Suppose f(x) = "6r V1+f dt.

A: Topic = Integration

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

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Q: Dt/dt = (h + bT)(T∞ − T), T(0) = To   To=1800K T∞=300K h=.025 b=10^-5 Find the explicit…

A: The differential equation is dTdt = (h + bT)(T∞ − T), T(0) = To The values are To=1800K, T∞=300K,…

Q: find the interval of the inicial value

A: Given Data: Let us consider the given data, t-6y'+t-2y=lnt+t-1 , y3=-4. To find the interval of…

Q: x'= -2y, y'= -4x, where primes indicate derivatives with respect to t, that satisfies the initial…

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Q: The function S(x.y)= (2x* + y^ )exp[ y + xy' is homogenous in x and y of degree 2x

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Q: Compute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2

A: To find the second derivative of f at x = 1. The approximation formula for second derivative at a…

Q: solve using ODE from t=0 to 2 when y(0)=1 dy/dt= yt^3 - 1.5y

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Q: Find the Fourier transform of the function y(t) if y(t) satisfies the differential equation d°y_dy…

A: First note that:  F-1e-5ω=12π∫-∞∞e-5ωejωtdω                       =12π∫-∞0e5ωejωtdω+12π∫0∞e-5ωejωtdω…

Q: f'(x) = = Lº 1 + sec(7t) dr f(x) = sec (2) + 6 X Vì Hint: +== f*√²- 1 + sec (7t) dt = - √1+ sec(71)…

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Q: Find the general solution to the linear ODE. Use each method (integrating factors and educated…

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Q: Solve y(x) for the Second Order ODE in parameter form: y"+7y'+10y=6e^3x

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Q: Find ect and the solution to X' = CX + (1) t X (0) = 0

A: X'=CX+1t1X0=000

Q: Fnd the solution to the initial value problem: dy/dt = (2t)/(y+t^(y)), y(0) = -2

A: Here the question should be , dy/dt=(2t)/(y+(t^2)y ) , y(0)=-2. I have solved it accordingly .…

Q: Solve the IVP to three decimal places when =. Check that your answer satisfies the ODE as well as…

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Q: For the given ODE: ) Convert the higher order ODE to a first order system in matrix form. i) Solve…

A: iwe have, y''+3y'+2y=0 Put x1t=yt x2t=y't ⇒x1'=y'=x2x2'=y''=-3y'-2y       from i…

Q: (D2 +DD'+D'-1) z = 0

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Q: Q3 By using the derivatives transformation find the transfer of the function a" (t) + æ(t) =…

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Q: Sketch the phase plane for x = x + 2y, y = 4|x| + Зу.

A: Here, we need to sketch the phase plane x˙=x+2y, y˙=4|x|+3y. Let us first find the critical points.…

Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: e'dy + (5t + ye')dt = 0.

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Q: dx |-

A: The problem is solved by substitution method. We substitute ex with y and solve the question by…

Q: y" − 3y' + 2y = 4e²t ; y(0) = −3, y '(0) = 5 —e2t4e2t + et 7 7 (1+t)4e²t - 7et 8e2t - 7et -e²t 4te²t…

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Q: Eliminate the arbitrary constant in the equatio y = cz +c +1 Oy= ry'+ (y') +1 O y =y'+(y')² +1 O'y=y…

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Q: Evaluate 2dy/dt + y = 0, y(0) = -3 Select the correct response: O y = 3 e^(t/2) O y = 3 e^(-t/2)…

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Q: The Impulse Response of a System is found to be t^e²t find the Transfer Function G(s).

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