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Questions on topic Differential Equation from Class 12 CBSE Maths

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Q1. 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)y + P(x)

dy/dx - P(x)y = Q(x)

Q2. What method is commonly used to solve homogeneous differential equations?

Substitution method

Integration factor

Separation of variables

Characteristic equation

Q3. The solution to the differential equation dy/dx = y is given by which of the following?

y = Ce^x

y = Cx

y = C/x

y = e^x + C

Q4. Which of the following is not a characteristic of a second-order linear differential equation?

It can have variable coefficients.

It has a degree of two.

It always has a unique solution.

It can be homogeneous or non-homogeneous.

Q5. If y = e^(3x) is a solution to the differential equation dy/dx - 3y = 0, what is the general solution?

y = Ce^(3x)

y = Ce^(-3x)

y = 3Ce^(3x)

y = Cx^3

Q6. What is the integrating factor for the equation dy/dx + 2y = 6?

e^(2x)

e^(-2x)

e^(6x)

e^(-6x)

Q7. Which of the following equations is a second-order differential equation?

dy/dx + y = 0

d²y/dx² + 4dy/dx + 4y = 0

dy/dx = x^2

dy/dx + 3y = 2x

Q8. The general solution of the differential equation d²y/dx² = 0 is:

y = C1x + C2

y = C1x^2 + C2

y = Ce^(x)

y = C1 + C2x

Q9. For the differential equation dy/dx = x^2y, which method is suitable for solving?

Linear method

Separation of variables

Exact equation

Substitution method

Q10. The characteristic equation for the differential equation d²y/dx² - 5dy/dx + 6y = 0 is:

r² - 5r + 6 = 0

r² + 5r + 6 = 0

r² - 6r + 5 = 0

r² + 6r + 5 = 0

Questions on topic Differential Equation from Class 12 CBSE Maths

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