Using Laplace transform methods, solve for t > 0 the fol- lowing simultaneous differential equations subject to the given initial conditions: dx dy 3. + dt - 2x = 3 sint + 5 cos t - dt dx 2- dt dy + y dt sint + cos t 0, where a is a real constant. subject to x = a and y = What value must a take to satisfy the set of simultaneous equations? -1 at t = |

Q: Using Laplace transform methods, solve for t > 0 the following differential equation, d²r d.r 5 + 6x…

A: The given initial value problem is d2xdt2-5dxdt+6x=2, x0=0, x'0=0. Solve the initial value problem…

Q: 2y" – 2y' + 2y = -cos(3t), y(0) = 0, y'(0) = 1 6.

A: Given differential equation is 2y''-2y'+2y=-cos(3t)                  (1) y(0)=0, y'(0)=1 Let the…

Q: V dv A model for the velocity v at time t of a certain object falling under the influence of gravity…

A: From the direction field We have to draw the sketch and See why v=16 is terminal velocity.

Q: Using the Laplace transform method, solve for t > 0 the following differential equation: d²x dx +3-…

A: The solution is given as

Q: The region bounded by f(x) 2x² + 12x + 14, x = = 0 is rotated about the y-axis. Find the volume of…

A: