Verify that y=sin 3t+2cos 3t is a solution to the initial value problem 2y"' +18y =...
Verify that y = sin 5t + 2cos 5t is a solution to the initial value problem 2y'' +50y = 0; y(0) = 2, y'(O) = 5. Find the derivatives of y. y' = Complete the verification below. + 50 = 0, which simplifies to 0 = 0. Check that y(0) = 2 by evaluating Insertion into 2y'' +50y = 0 gives 2 and check that y'(0) = 5 by evaluating
Find the solution of the given initial value problem: 2y‴+18y′−540y=0 y(0)=10, y′(0)=54, y″(0)=−306 Enclose arguments of functions in parentheses. For example, sin(2x).
Use the Laplace transform to solve the following initial value problem: 44" + 2y + 18y = 3 cos(3t), y(0) = 0, y(0) = 0. a. First, take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation and then solve for L{y(t)}. Do not perform partial fraction decomposition since we will write the solution in terms of a convolution integral. 3s L{y(t)}(s) = (452 + 25 +2s + 18)(52+9) b. Express the...
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(****+})
Find the solution of the given initial value problem in explicit form. y′=(9x)/(y+x^2y), y(0)=−3 Enclose arguments of functions in parentheses. For example, sin(2x).
dy Find solution for initial valued problem:-3y + 2 3t ,y(0)--1 dt dy Find solution for initial valued problem:-3y + 2 3t ,y(0)--1 dt
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...
Find y(t) solution of the initial value problem 3t y? Y' – 6 y3 – 4t² = 0, y(1) = 1, g(1)=1, t > 0.