1. What is the order of the differential equation? 2y + 1 y" (b) y'y(4) + t²y³ = (sin y)y' (c) √(")4+1² - evy' = Int 2.

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1 What Is The Order Of The Differential Equation 2y 1 Y B Y Y 4 T Y Sin Y Y C 4 1 Evy Int 2 1 (45.63 KiB) Viewed 27 times

1. What is the order of the differential equation? 2y + 1 y" (b) y'y(4) + t²y³ = (sin y)y' (c) √(")4+1² - evy' = Int 2. Determine whether the given function is a solution to the given differential equation. y + y² = et+ (1-2t)e+t2 +1 y" - 2y + 2y = e' sin t (a) e'y' + + 3t = y¹ (a) y(t) = e¹+t, (b) y(t) = 3 sin(2t) + e-t, 3. (a) Show that y(t) = Cie-2t + C₂e5t - 2 is a solution of the differential equation y" - 3y 10y = 20, where C₁ and C₂ are arbitrary constants. (b) Use part (a) to find a function that satisfies the given conditions: y" - 3y - 10y = 20, y(0) = 4, lim y(t) = -2 t-00 4. (a) Determine if each of the following equations is autonomous and find all equilibrium solutions (if any), (b) sketch the direction field in the given rectangular plane of the ty- plane, and (c) sketch a rough solution curve at the given point. (Show matching slope numbers) (i) y = y²-3y -4 at (0, 1) in 0 ≤t≤4 and -2 ≤ y ≤ 4 (ii) y = t²-y at (-2,0) in -3 ≤ t ≤ 3 and 0 ≤ y ≤ 3