Degree of a Differential Equations

Q. The degree and order of the differential equation of the family of all parabolas whose axis is x–axis, are respectively

1. 1, 2
2. 3, 2
3. 2, 3
4. 2, 1

Q. Degree of the differential equation
$\frac{d^{4}y}{d{x}^4}+(\frac{d^{3}y}{d{x}^3}{)}^2+(\frac{d^{2}y}{d{x}^2}{)}^3+(\frac{dy}{dx}{)}^4=0$ is ___

Q. Degree of the differential equation $\frac{d^{2}y}{d{x}^2}=\sqrt[3]{31+(\frac{dy}{dx}{)}^4}$ is ___

Q. The degree of the differential equation $3\frac{d^{2}y}{d{x}^2}={\{1+{\left(\frac{dy}{dx}\right)}^2\}}^{3/2}$ is

1. 1
2. 2
3. 3
4. 6

Q. If p and q are order and degree of differential equation $y^2(\frac{d^{2}y}{d{x}^2}{)}^2+3x(\frac{dy}{dx}{)}^{\frac{1}{3}}+x^2{y}^2=sinx$, then

1. $p>q$
2. $\frac{p}{q}=\frac{1}{2}$
3. $p=q$
4. $p<q$

Q.

The order and degree of the differential equation $y=x\frac{dy}{dx}+\sqrt{a^2{\left(\frac{dy}{dx}\right)}^2+b^2}$ are

1. 1, 2

2. 2, 1

3. 1, 1

4. 2, 2

Q. The degree of the differential equation $\frac{d^{2}y}{d{x}^2}+3{\left[\frac{dy}{dx}\right]}^2=x^{2}log\left[\frac{d^{2}y}{d{x}^2}\right]$ is

1. 1
2. None of these
3. 3
4. 2

Q. The order and degree of the differential equation ${(1+3\frac{dy}{dx})}^{\frac{2}{3}}=4\frac{d^{3}y}{d{x}^3}$ are

1. 3, 1
2. 3, 3
3. 1, 2
4. $1,\frac{2}{3}$

Q.

The order and degree of the differential equation ${[4+{\left(\frac{dy}{dx}\right)}^2]}^{2/3}=\frac{d^{2}y}{d{x}^2}$ are

1. 2, 2

2. 3, 3

3. 2, 3

4. 3, 2

Q. The degree of the differential equation satisfying $\sqrt{1+x^2}+\sqrt{1+y^2}=A(x\sqrt{1+y^2}-y\sqrt{1+x^2})$

1. 2
2. None of these
3. 3
4. 4