The solution of \(\frac{dy}{dx}\) = 1 + x + y + xy is

log (1 + y) = x + \(\frac{x^2}{2}\) + k

log (1 + x) + y + \(\frac{y^2}{2}\) = k

\(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) + 2y = 0

\(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) = 0

\(\frac{d^2y}{dx^2}\) – 2\(\frac{dy}{dx}\) + 2y = 0

\(\frac{d^2y}{dx^2}\) + 2\(\frac{dy}{dx}\) + 2y = 0

The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants is

\(\frac{d^2y}{dx^2}\) + α²y = 0

\(\frac{d^2y}{dx^2}\) – α²y = 0

\(\frac{d^2y}{dx^2}\) + α²y = 0

\(\frac{d^2y}{dx^2}\) + αy = 0

\(\frac{d^2y}{dx^2}\) – αy = 0

CBSE Class 12 Maths Differential Equations Quiz 1

9.

Solution of differential equation xdy – ydx = Q represents

a rectangular hyperbola

parabola whose vertex is at origin

straight line passing through origin

a circle whose centre is at origin

1.

Integration factor of differential equation $\frac{dy}{dx}$ + py = Q, where P and IQ are functions of x is

2.

The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is

3.

The solution of $\frac{dy}{dx}$ = 1 + x + y + xy is

4.

The degree of the differential equation

5.

The degree of differential equation[1 + ( $\frac{dy}{dx}$ )²]= $\frac{d^2y}{dx^2}$ is

6.

The order and degree of the differential equation $\frac{d^2y}{dx^2}$ + ( $\frac{dy}{dx}$ )+ x= 0 respectvely, are

7.

If y = e

8.

The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants is

9.

Solution of differential equation xdy – ydx = Q represents

10.

Integrating factor of the differential equation cos x $\frac{dy}{dx}$ + y sin x = 1 is

Time

0 h : 0 m : 1 s

1. Integration factor of differential equation dydx\frac{dy}{dx} + py = Q, where P and IQ are functions of x is

2. The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is

3. The solution of dydx\frac{dy}{dx} = 1 + x + y + xy is

4. The degree of the differential equation

5. The degree of differential equation[1 + (dydx\frac{dy}{dx})²]= d2ydx2\frac{d^2y}{dx^2} is

6. The order and degree of the differential equation d2ydx2\frac{d^2y}{dx^2} + (dydx\frac{dy}{dx})+ x= 0 respectvely, are

7. If y = e

8. The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants is

9. Solution of differential equation xdy – ydx = Q represents

10. Integrating factor of the differential equation cos x dydx\frac{dy}{dx} + y sin x = 1 is

Time

0 h : 0 m : 1 s

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1.

Integration factor of differential equation $\frac{dy}{dx}$ + py = Q, where P and IQ are functions of x is

2.

The radius of a circle is increasing at the rate of 0.4 cm/ s. The rate of increasing of its circumference is

3.

The solution of $\frac{dy}{dx}$ = 1 + x + y + xy is

4.

The degree of the differential equation

5.

The degree of differential equation[1 + ( $\frac{dy}{dx}$ )²]= $\frac{d^2y}{dx^2}$ is

6.

The order and degree of the differential equation $\frac{d^2y}{dx^2}$ + ( $\frac{dy}{dx}$ )+ x= 0 respectvely, are

7.

If y = e

8.

The differential equation for y = A cos αx + B sin αx where A and B are arbitary constants is

9.

Solution of differential equation xdy – ydx = Q represents

10.

Integrating factor of the differential equation cos x $\frac{dy}{dx}$ + y sin x = 1 is