Mid-2 DE ( major& minor)
Authored by Aruna Sadasivuni
Mathematics
University
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15 questions
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1.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
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
2.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
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)
3.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
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
4.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
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)
5.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
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)
6.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
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)
7.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
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)
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