3. (20 points) Find the solution y = y(x) of the initial value problem y 0 − y x = cos2 (y/x) , y(1) = π 3
3. (20 points) Find the solution y = y(x) of the initial value problem y 0...
Question 1: (20 points) Find the solution of the initial value problem a = cos? x – sin x – 2y cos x + y2 , y(0) = given that yi(2) = cos x is a solution of the differential equation.
Find the solution to the initial value problem: dy dy/dx=x^ 2√1 + x^3/1+cos y y(0)=2 the 1+x^3 is all in square root.
1. (5 points) Find an interval containing x 0for which the given initial value problem has a unique solution. y=x2 +2 +cos(x 1. (5 points) Find an interval containing x 0for which the given initial value problem has a unique solution. y=x2 +2 +cos(x
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
Question 6 (3 points) Find y(t) solution of the initial value problem y" + 8 y' + 20 y = -4 8(t – 2), y(0) = 0,
Find the solution of the given initial value problem. y" + 2y' +2y = cost+8(-5); y(0) = 3, y'(0) = 5 ° 20) = us20e" sin + + cost ( +ş) + sint (36+}) x() ==««n6e8cose + cost (3e* +) + sint (80* + }) 20 = usz beé" sin + sing (54* +5.) +cos (34++}) ° 40 = =uaz(Dei* cost + cost ("* + 5 ) + sint (3*+ }) 209 = 192(e“ cose + cost (* +) +sint(****+})
Consider the initial value problem for function y, y" – ' - 20 y=0, y(0) = 2, 7(0) = -4. a. (4/10) Find the Laplace Transform of the solution, Y(8) = L[y(t)]. Y(8) = M b. (6/10) Find the function y solution of the initial value problem above, g(t) = M Consider the initial value problem for function y, Y" – 8y' + 25 y=0, y(0) = 5, y(0) 3. a. (4/10) Find the Laplace Transform of the solution. Y(s)...
2. (5 points) Find the solution of the following Initial Value Problem dy +9=1, y(0) = 1
Exact Differential Equations. Let y(x) be the solution of the following initial value problem: (cos z ln(2y = 8) + 2) + (x+4)=0, x(1) -- What is the value of y(+/2)? (a) 37 + 1. (b) 1/7- 2. (c) /3+ V. (d) 4+1/. (e) None.
6. Solve the initial value problem y" + y = 0, y(0)=0, y'0=1 (a) -COS X (b) -sin x (c) -sin x + cos x (d) -sin x COS X (e) COS X (f) sin x (g) sin x-COS X (h) sin x + cos x 7. Find a particular solution yn of the differential equation (using the method of undetermined coefficients): y + y =p2 (a) 2e (b) 3e (c) 4e: (d) 6e (e) 2/2 (f) e2/3 (g) e2/4...