Differential Equations
Math ⇒ Calculus
Differential Equations starts at 12 and continues till grade 12.
QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Differential Equations.
How you perform is determined by your score and the time you take.
When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.
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 equation: \frac{dy}{dx} = \frac{1}{x+1}, y(0) = 2.
State the difference between a general solution and a particular solution of a differential equation.
State the general solution of the differential equation \frac{dy}{dx} = k, where k is a constant.
State the integrating factor for the equation \frac{dy}{dx} + \frac{1}{x}y = x.
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.
Explain the difference between a linear and a non-linear differential equation, providing an example of each.
Given the initial value problem \frac{dy}{dx} = 3y , y(1) = 2 , find the explicit solution for y in terms of x .
Prove that the function y = Ce^{-2x} is a solution to the differential equation \frac{dy}{dx} + 2y = 0 .
Solve the differential equation: \frac{dy}{dx} + 2y = e^{2x} , given that y(0) = 1 .
