Degree of a Differential Equations

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

1. 1
2. 2
3. 3
4. none of these

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. 2
3. 3
4. None of these

Q. Let omega= cos 3 degree+isin 3 degree then summation(r=1 to 10)(Re(omega^(2r-1))) equals

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

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

Q. The 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. $\frac{d^{3}y}{{\mathrm{dx}}^3}+\mathrm{cosy}\frac{\mathrm{dy}}{\mathrm{dx}}=0$

Q. The differential equation of the family of curves $y=e^x(A\cos x+B\sin x),$ where $A$ and $B$ are arbitrary constants, is

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