For the DDS given by yn+1 = Ус -0.5y + 30, find the equilibrium value.
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- Differentiate y = (2x + 1) а. 2 y (2x + 1) b. 1 y 2/(2x + 1) 1 y = (2х + 1) d. y = -V(2x + 1) %3D е. -1 y = V(2x + 1)Find the equilibrium solutions and determine which are stable and which are unstable. y' = 9y – 3y? O y=-3 (stable); y = 0 (unstable) y = 0 (unstable); y=3 (stable) y = 0 (stable); y = 3 (unstable) y=-3 (unstable); y = 0 (stable)Q5. Write the governing equation of 1-D heat transfer with convective heat loss and indicate all the parameters involved in it.
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- Solve the following first order equations: (e* + y)d.x + (2+ x + ye")dy = 0, y(0) = 1.State whether the equation is ordinary or partial, linear or nonlinear and determine its order and degree. d?x 1. dt2 + k²x = 0 2 4 (dw 2. ( - 2' + yw = 0 dx² dx 3. у" — Зу' + 2у %3D0 a²u 4. ax2 a?u = 0 ду? SITYShow that the smoking free equilibrium E0 = (P0, S0, Qt0 ) = (1, 0, 0) and the smoking present equilibrium E* = (P *, S* , Q* t ), by setting the right-hand side of the equations in the model tozero.