Differential Equations
Math ⇒ Calculus
Differential Equations starts at 12 and continues till grade 12.
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See sample questions for grade 12
A population P(t) grows at a rate proportional to its size. Write the differential equation representing this situation.
A tank contains 100 liters of water and salt is added at a rate of 2 grams per minute. If the tank is well-mixed and water flows out at the same rate, write the differential equation for the amount of salt S(t) in the tank at time t.
Solve the differential equation dy/dx = 3x2.
Solve the equation: dy/dx + y = 0, y(0) = 2.
Solve the equation: dy/dx = 1/(x+1), y(0) = 2.
A population P(t) grows at a rate proportional to its size. Write the differential equation representing this situation.
A tank contains 100 liters of water and salt is added at a rate of 2 grams per minute. If the tank is well-mixed and water flows out at the same rate, write the differential equation for the amount of salt S(t) in the tank at time t.
A radioactive substance decays at a rate proportional to the amount present. If 80 grams are present initially and 20 grams remain after 10 hours, find the time (in hours) when only 5 grams will remain.
Which method is most suitable for solving the equation dy/dx = (x2 + y2)/(2xy)?
(1) Separation of variables
(2) Homogeneous substitution
(3) Integrating factor
(4) None of these
Which of the following best describes a general solution?
(1) A solution with no arbitrary constants
(2) A solution with one or more arbitrary constants
(3) A solution that satisfies initial conditions
(4) None of the above
Which of the following is a first-order differential equation?
(1) y'' + y = 0
(2) y' + y = 0
(3) y''' + 2y' = 0
(4) y'' - y' + y = 0
Which of the following is a homogeneous differential equation?
(1) dy/dx = (x + y)/(x - y)
(2) dy/dx = x2 + y
(3) dy/dx = x/y
(4) dy/dx = x + y
Fill in the blank: The general solution of dy/dx = cos(x) is y = _______.
Fill in the blank: The integrating factor for dy/dx + y = x is _______.
Fill in the blank: The integrating factor for the linear equation dy/dx + P(x)y = Q(x) is _______.
Fill in the blank: The order of the differential equation d3y/dx3 + 2y = 0 is _______.
True or False: The equation d2y/dx2 + 2dy/dx + y = 0 has a general solution of the form y = (A + Bx)e-x.
True or False: The equation d2y/dx2 + 4y = 0 is a second-order linear homogeneous differential equation.
True or False: The equation dy/dx + y = ex is a non-homogeneous linear differential equation.
True or False: The equation dy/dx = x + y is linear.
