WorksheetsMid-2 DE ( major& minor)
Total questions: 15
Worksheet time: 30mins
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)
To find solutions for the higher order DE, with variable coefficients which method we use
Variation parameters
Cauchy Euler method
Both the above
None of the above
Find the particular solution of y'' + 3y' + 2y = cos(x).
y_p = -1/5 cos(x)
y_p = 1/5 cos(x)
y_p = 1/10 (cost + 3 sint)
y_p = 1/5 sin(x)
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)
Find the general solution of y'' - 6y' + 9y = e^t
y(t) = (C1 + C2t)e^(3t)+1/4(e^t)
y(t) = C1e^(3t) + C2e^(3t)
y(t) = C1e^(2t) + C2e^(4t)+1/4(e^t)
y(t) = C1e^(3t) + C2t^2e^(3t)
Solve the equation y'' + y = 0.
y(t) = C1 sint + C2 cost
y(t) = C1*e^(-t) + C2*e^(-2t)
y(t) = C1*e^(2t) + C2*e^(t)
y(t) = C1*e^(3t) + C2*e^(t)
