For which value of a the system of ODEs ỷ₁ = sinh(y₁) + a tanh(y₂), y₂ = −2 cos(y₁) + 2e³¹+½ + tanh(y₂), linearised around (y₁, y₂) = (0,0) displays an unstable focus? Select one: a. −1/2 < a < 0 O b. a = 2 O c. 0 < a <2 O d. a < -1/2

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Q: 11. Which function has the shortest period? A. y 6 sin(3x) + 20 B. y = 8 cos(2x) - 4 С. y 7 соs(x) +…

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Q: 4. Solve the ODE using Separation of Variables. X. dy - y = 2x²y dx

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Q: Find the value(s) of ß for which y (t) = cos(ßt) satisfies y” + 100y = 0

A: Given that yt=cosβt satisfies the equation y''+100y=0. We have to find the values of β.

Q: 4. In each part below, find dy dx a. y=x³ +5* +55

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

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