Differential Equations Quiz - Class XII
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Preview questions
1. What is the general form of a first-order linear differential equation?
dy/dx + P(x)y = Q(x) · dy/dx = P(x)y + Q(x) · dy/dx = Q(x) - P(x)y · dy/dx + Q(x) = P(x)y
2. Which method is used to solve homogeneous differential equations?
Substitution method · Integrating factor method · Separation of variables · Variation of parameters
3. What is the integrating factor for the equation dy/dx + 2y = 3x?
e^(2x) · e^(-2x) · e^(3x) · e^(-3x)
4. Identify the order of the differential equation: d^2y/dx^2 + 3dy/dx + 2y = 0.
First order · Second order · Third order · Zero order
5. Which of the following is a characteristic of a separable differential equation?
Can be expressed as f(y)dy = g(x)dx · Has constant coefficients · Is always linear · Can be solved using Laplace transforms
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