CBSE Class 12 Maths Differential Equations Quiz 3

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CBSE › Class 12 › Maths › Differential Equations

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1. The solution of \(\frac{dy}{dx}\) + y = e, y (0) = 0 is

A y = e(x – 1) B y = xe C y = xe+ 1 D y = (x + 1 )e

2. Integrating factor of the differential equation \(\frac{dy}{dx}\) + y tan x – sec x = 0 is

A cos x B sec x C e D e

3. The solution of the differential equation \(\frac{dy}{dx}\) = \(\frac{1+y^2}{1+x^2}\)

A y = tan x B y – x = k(1 + xy) C x = tan y D tan (xy) = k

4. The integrating factor of the differential equation \(\frac{dy}{dx}\) + y = \(\frac{1+y}{x}\) is

A \(\frac{x}{e^x}\) B \(\frac{e^x}{x}\) C xe D e

5. y = ae+ be satisfies which of the following differential equation?

A \(\frac{dy}{dx}\) + my = 0 B \(\frac{dy}{dx}\) – my = 0 C \(\frac{d^2y}{dx^2}\) – m²y = 0 D \(\frac{d^2y}{dx^2}\) +m²y = 0

6. The solution of the differential equation cos x sin y dx + sin x cos y dy = 0 is

A \(\frac{sin x}{sin y}\) = c B sin x sin y = c C sin x + sin y = z D cos x cos y = c

7. The differential equation of the family of cuves x² + y² – 2ay = 0, where a is arbitrary constant is

A (x² – y²)\(\frac{dy}{dx}\) = 2xy B 2 (x² + y²)\(\frac{dy}{dx}\) = xy C 2(x² – y²)\(\frac{dy}{dx}\) = xy D (x² + y²) \(\frac{dy}{dx}\) = 2xy

8. Family y = Ax + A³ of curves will correspond to a differential equation of order

A 3 B 2 C 1 D not finite

9. The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is

A an ellipse B parabola C circle D rectangular hyperbola

10. The general solution of the differential equation \(\frac{dy}{dx}\) = e

A y = ce B y = ce C y = (x + c)e D y = (c – x)e

Practice more on Differential Equations

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