Consider the initial value problem Suppose we know that y(t) → 0 as t→∞o. Determine the solution and the initial conditions. y(t) = = y(0) = y'(0) = help (formulas) y" +36y=e, y(0) = yo, y'(0) = yo. help (numbers) help (numbers)

Q: y''=-y-y'+1/(4-y). Determine if there are any equilivrium solutions, and, if so, waht they are.

A: To find the equilibrium points we first convert the second order ODE into two first order ODE then…

Q: (c) 2ry'y-y²+²=0.

A: 2xy'y-y2+x2=0⇒2xyy'=y2-x2

Q: Solve y + y = 2y = 0, where y (0) - = 3 and y (0 y(t) =

A: y''+y'-2y=0 Auxiliary eqaution m2+m-2=0

Q: Find the solution to if x (0) = 0 and y(0) = 4. x(t) = y(t) = x' y' help (formulas) help (formulas)…

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Q: Solution: y1 = 1.450000000; y2= 2:085625000; y3 = 3:079099746

A: Here, initial condition is given at x = 2.Therefore, start with x0 = 2.Given equation is:

Q: Let y'= 2xy²; y=- 1 36-x² y(5)= 11 differential equation, give at least one interval I of…

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Q: " + y' + y = x? - 4x 13 y(x) : 2x + 8

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Q: dy (2² + 9) + æy - = 0 da

A: To determine limit x tends to infity y(x) for the given differential equation

Q: Consider the initial value problem y'=y(8- ty), yo = y(0). Observe that for yo = 0, y = 0 is an…

A: Given, the initial value problem is:with and equilibrium solution for y0=0 i.e., y=0 is an…