Verify that y = sin 5t + 2cos 5t is a solution to the initial value...
Verify that y=sin 3t+2cos 3t is a solution to the initial value problem 2y"' +18y = 0; y(0) = 2, y' (O) = 3. Find the derivatives of y. y' = y" Complete the verification below. and check that y'(0) = 3 Insertion into 2y" + 18y = 0 gives 2O +18 = 0, which simplifies to 0 = 0. Check that y(0) = 2 by evaluating by evaluating
hellllllllllp please a) Verify that the function y = ?? + is a solution of the differential equation zy' +2y 4x? (x > 0). b) Find the value ofe for which the solution satisfies the initial condition (2) - 5. = Submit Question a) Verify that the function y=x? + с 2 is a solution of the differential equation ry' + 2y = 4x², (x > 0). b) Find the value of c for which the solution satisfies the initial...
B) Use the Laplace transform to solve the given initial-value problem: y' + 2y = 2cos(2+), with y(0) = 1
Find the solution of the given initial value problem: y(4) + 2y" + y y(3) (0) y, (0) 0, y', (0) llt + 2; y (0) 1 Enclose arguments of functions in parentheses. For example, sin (2x) Find the solution of the given initial value problem: y(4) + 2y" + y y(3) (0) y, (0) 0, y', (0) llt + 2; y (0) 1 Enclose arguments of functions in parentheses. For example, sin (2x)
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(****+})
art 1 sin(5t)) z(t) = (cos(50t) + x(t))?, where x(t) = }. z(t) is passed through a filter with impulse response h(t) in order to pass only the product 2x(t) cos(50t). Which filter below is the correct filter to do that? ST sin(5t) sin(15t) / (a) h(t) = {* tt at (b) h(t) sin(5t) sin(100) L 1. Tt at os(1004) 5 it - Tt J (c) h(t) = {i sinft) sin15)} 2cos(50) (a) h(e) = { i sin tuon )*2...
Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y' + 5y = 5t? -9, y(0) = 0, y'(0) = -3 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. 169=122 3.sin (1960) - cos (15) -
(a) Verify that all members of the family y (5)1/2 (c- x2)-1/2 are solutions of the differential equationy y (b) Find a solution of the initial-value problem (a) Verify that all members of the family y (5)1/2 (c- x2)-1/2 are solutions of the differential equationy y (b) Find a solution of the initial-value problem
Q4 please 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find a particular solution of the equation y" +2/ +2y = sin 2x by method of undetermined coeficients. 4 marks] (c) Use Laplace transform to solve the initial value problem l-1, 21 0-,0)- [10 marks] 4. (a) Find the general solution of the equation y" +2y +2y tan by varia- tion of parameters 6 marks] (b) Find...
1. Find the particular solution of the differential equation dydx+ycos(x)=2cos(x)dydx+ycos(x)=2cos(x) satisfying the initial condition y(0)=4y(0)=4. 2. Solve the following initial value problem: 8dydt+y=32t8dydt+y=32t with y(0)=6.y(0)=6. (1 point) Find the particular solution of the differential equation dy + y cos(x) = 2 cos(z) satisfying the initial condition y(0) = 4. Answer: y= 2+2e^(-sin(x)) Your answer should be a function of x. (1 point) Solve the following initial value problem: dy ty 8 at +y= 32t with y(0) = 6. (Find y as...