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2) Sketch the phase portrait of the system x' (t) = Ax (t) if (a) 5=...
Could someone explain how these to get these phase portraits by hand with ẋ=y and ẏ=ax-x^2...
Could someone explain how these to get these phase portraits by
hand with ẋ=y and ẏ=ax-x^2 especially for a=0 case where you have
eigenvalues all equal to zero?
6.5.4 a>0 Sketch the phase portrait for the system x = ax-x, for a < 0, a = 0, and For a -(0 We were unable to transcribe this imageFor a>0 ES CS
Consider the linear system of first order differential equations x' = Ax, where x = x(t),...
Consider the linear system of first order differential equations x' = Ax, where x = x(t), t > 0, and A has the eigenvalues and eigenvectors below. Sketch the phase portrait. Please label your axes. 11 = 5, V1 = 12 = 2, V2 = ()
For #1 and #2, find the general solution of the ODE system tX' = AX, t>...
For #1 and #2, find the general solution of the ODE system tX' = AX, t> 0. (You do NOT need to verify that the Wronskian is nonzero.) 1. A= ( 1)
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t...
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
Extra Credit Question:[4+4=8 pts) If E [exp(aX)] exists for a given constant a, then show that...
Extra Credit Question:[4+4=8 pts) If E [exp(aX)] exists for a given constant a, then show that for to (a) exp(-at)P(x >t) <E (exp(aX)], if a > 0. (b) exp(-at)P(X <t) <E (exp(aX)], if a < 0.
10) The X random variable has a normal distribution. P(X > 15) = 0.0082 and P(X<5)...
10) The X random variable has a normal distribution. P(X > 15) = 0.0082 and P(X<5) = 0.6554 find the mean and variance of this distribution
2. If X and Y are independent random variables, X has a normal distribution with mean...
2. If X and Y are independent random variables, X has a normal distribution with mean 2 variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find u such that P(X > 2+11,7)=0.01.
Sketch curves of x-1 versus T for T > Tc for (a) a paramagnet, (b) a...
Sketch curves of x-1 versus T for T > Tc for (a) a paramagnet, (b) a ferromagnet, and (c) an antiferromagnet, and discuss the meaning of the intercept on the T axis.
5. Consider the system in the figure below with X (12) = 0 for 221 >...
5. Consider the system in the figure below with X (12) = 0 for 221 > 20007, and the discrete-time system a squarer, i.e. yn = t[n]. What is the largest value of T such that y(t) = I.(t)? x[n] Hiscrete-time y[n] system D/C
Problem 5: The switch in the network below opens at t-0s. Solve o(t) for t> Os...
Problem 5: The switch in the network below opens at t-0s. Solve o(t) for t> Os 七"OS. 2kn 2-5t Answer: 10 (t)--e-mA, t 〉 0 (note: τ = 9/5 s = 1.8s) 3
Could someone explain how these to get these phase portraits by
hand with ẋ=y and ẏ=ax-x^2 especially for a=0 case where you have
eigenvalues all equal to zero?
6.5.4 a>0 Sketch the phase portrait for the system x = ax-x, for a < 0, a = 0, and For a -(0 We were unable to transcribe this imageFor a>0 ES CS
Consider the linear system of first order differential equations x' = Ax, where x = x(t), t > 0, and A has the eigenvalues and eigenvectors below. Sketch the phase portrait. Please label your axes. 11 = 5, V1 = 12 = 2, V2 = ()
For #1 and #2, find the general solution of the ODE system tX' = AX, t> 0. (You do NOT need to verify that the Wronskian is nonzero.) 1. A= ( 1)
Consider the linear system of first order differential equations x' = Ax, where x= x(t), t > 0, and A has the eigenvalues and eigenvectors below. 4 2 11 = -2, V1 = 2 0 3 12 = -3, V2= 13 = -3, V3 = 1 7 2 i) Identify three solutions to the system, xi(t), xz(t), and x3(t). ii) Use a determinant to identify values of t, if any, where X1, X2, and x3 form a fundamental set of...
Extra Credit Question:[4+4=8 pts) If E [exp(aX)] exists for a given constant a, then show that for to (a) exp(-at)P(x >t) <E (exp(aX)], if a > 0. (b) exp(-at)P(X <t) <E (exp(aX)], if a < 0.
10) The X random variable has a normal distribution. P(X > 15) = 0.0082 and P(X<5) = 0.6554 find the mean and variance of this distribution
2. If X and Y are independent random variables, X has a normal distribution with mean 2 variance 4, and Y has a chi-square distribution with 9 degrees of freedom, then find u such that P(X > 2+11,7)=0.01.
Sketch curves of x-1 versus T for T > Tc for (a) a paramagnet, (b) a ferromagnet, and (c) an antiferromagnet, and discuss the meaning of the intercept on the T axis.
5. Consider the system in the figure below with X (12) = 0 for 221 > 20007, and the discrete-time system a squarer, i.e. yn = t[n]. What is the largest value of T such that y(t) = I.(t)? x[n] Hiscrete-time y[n] system D/C
Problem 5: The switch in the network below opens at t-0s. Solve o(t) for t> Os 七"OS. 2kn 2-5t Answer: 10 (t)--e-mA, t 〉 0 (note: τ = 9/5 s = 1.8s) 3
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