27. Solve the given differential equation. (a) (y2 + 1)dr - ysec2 zdy (b) g(In -In g)dz (rIna- Iny - y)dy (c) (6x +1)3?+ 3x2 + 2y3 =0 ar () nt (f) (2x + y +1)y -1 (g) (2,2 + 4)dy = (2z-8zydr (h) (2r2 cos θ sin θ+ r cos θ)d2+ (4r+sin θ-2r cos20)dr dQ dt
d1 dy 2. Solve the system dt dt2 da dt =t = 2 dy (25pts) + 3x + + 3y = dt
Use the Laplace transform to solve dy cost + So y(t) cos(t – t)dt, y(0) = 1 dt
(1 point) A. Solve the following initial value problem: dy dt cos (t)-1 with y(6) tan(6). (Find y as a function of t.) (1 point) A. Solve the following initial value problem: dy dt cos (t)-1 with y(6) tan(6). (Find y as a function of t.)
Solve for y(t). dy/dt + 2x = et dx/dt-2y= 1 +t when x(0) = 1, y(0) = 2
Questions 4-5: An LTIC system can be described by an equation: dy(t) dr 2 + 2x(t) dt? 4. What will be the zero-input response y(i), if the initial conditions are yo (0) = 0, and Y. (O) = 12 A). y.(t) = e" + B). y(t)=en-ex C). y.(t)=e-2 -2% D). y(t) = -2-2 +e-3 The transfer function of the LTIC system can be calcu . If the input signal of the system is x(t) = 8(6), what will as H(m)...
Solve the given system of differential equations by systematic elimination. dx dt = 2x − y dy dt = x (x(t), y(t)) =
Solve the system of differential equations. Include a phase plane and discuss the stability of the equilibrium. (dx)/(dt) = 2x+2y, (dy)/(dt)=15x-5y d.r dt 152-by dt d.r dt 152-by dt
Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the general solution of the system (c) Solve the initial value problem given (0) 3 and y(0)-4 (d) Verify the calculations with MATLAB Question 3 Consider the following linear system of differential equations dx: = 2x-3y dt dy dt (a) Write this system of differential equations in matrix form (b) Find the...
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt