Mid-2 DE ( major& minor)

Solve the equation y''' - 3y'' + 2y = 0.

• y(t) = C1*e^(t) + C2*e^(2t)

• y(t) = C1*e^(-t) + C2*e^(-2t) + C3

• y(t) = C1*e^(2t) + C2*e^(t) + C3*e^(t)

• y(t) = C1*e^(3t) + C2*e^(t) + C3

Find the general solution of y'''' + 4y'' = 0.

• y(t) = C1 + C2*t + C3*e^(2t) + C4*e^(-2t)

• y(t) = C1 + C2*t + C3*cos(2t) + C4*sin(2t)

• y(t) = C1 + C2*t^2 + C3*cos(t) + C4*sin(t)

• y(t) = C1 + C2*t + C3*cos(3t) + C4*sin(3t)

Determine the particular solution for y'' + 5y' + 6y = e^x.

• y_p = (1/6)e^x

• y_p = (1/24)e^x

• y_p = (1/12)e^x

• y_p = (1/3)e^x

Solve the differential equation y'' - 4y' + 4y = 0 with initial conditions y(0) = 1, y'(0) = 0.

• y(t) = (1 - t)e^(2t)

• y(t) = e^(2t)

• y(t) = (1 + t)e^(2t)

• y(t) = t^2e^(2t)

Find the complementary function of y'' + 2y' + y = 0.

• y_c = C1 * e^(-x) + C2 * x * e^(-x)

• y_c = C1 * e^(-2x) + C2 * e^(-x)

• y_c = C1 * x + C2 * x^2

• y_c = C1 * e^(x) + C2 * x * e^(x)

Solve the equation y''' + 2y'' - y' - 2y = 0.

• y(t) = C1 * e^(t) + C2 * e^(2t) + C3 * e^(-t)

• y(t) = C1 * e^(-t) + C2 * e^(-2t) + C3 * e^(t)

• y(t) = C1 * e^(2t) + C2 * e^(-t) + C3 * e^(t)

• y(t) = C1 * e^(t) + C2 * e^(-t) + C3 * e^(-2t)

Determine the general solution for y'''' - 2y'' = 0.

• y(t) = C1 + C2*t^2 + C3*e^(2t) + C4*e^(-2t)

• y(t) = C1 + C2*ln(t) + C3*t^2 + C4*e^(t)

• y(t) = C1 + C2*t + C3*e^(sqrt(2)t) + C4*e^(-sqrt(2)t)

• y(t) = C1*e^(sqrt(2)t) + C2*e^(-sqrt(2)t)

Find the particular solution of y'' + 3y' + 2y = sin(x).

• y_p = 1/10 (sint -3 cost)

• y_p = 1/5 cos(x)

• y_p = -1/5 sin(x)

• y_p = 1/5 sin(x)

Solve the equation y'' + 4y = 0 with initial conditions y(0) = 0, y'(0) = 1.

• y(t) = (1/4)sin(4t)

• y(t) = (1/2)cos(2t)

• y(t) = (1/2)sin(2t)

• y(t) = cos(2t)

Find the general solution of y'' - 6y' + 9y = 0.

• y(t) = (C1 + C2t)e^(3t)

• y(t) = C1e^(3t) + C2e^(3t)

• y(t) = C1e^(2t) + C2e^(4t)

• y(t) = C1e^(3t) + C2t^2e^(3t)