Degree of a Differential Equations

Q.

The degree of the differential equation satisfying $\sqrt{1-x^4}+\sqrt{1-y^4}=a(x^2-y^2)$, is

1. 1

2. 2

3. 3

4. None of these

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

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. The degree of is not well defined.

1. $\frac{d^{3}y}{{\mathrm{dx}}^3}+\frac{\mathrm{dy}}{\mathrm{dx}}=e^y$
2. $e^{\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}=k+\frac{\mathrm{dy}}{\mathrm{dx}}$
3. $\sqrt{\left(1+{\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2\right)}=y\frac{d^{3}y}{{\mathrm{dx}}^3}$
4. $\frac{d^{3}y}{{\mathrm{dx}}^3}+\mathrm{cosy}\frac{\mathrm{dy}}{\mathrm{dx}}=0$