Homogeneous Differential Equation

Q.

The solution of the differential equation $\frac{dy}{dx}=\frac{1+y^2}{1+x^2}$ is

[SCRA 1986]

1. $1+xy+c(y+x)=0$
2. $x+y=c(1-xy)$
3. $y-x=c(1+xy)$
4. $1+xy=c(x+y)$

Q. The solution of the differential equation $x\frac{dy}{dx}=y(logy-logx+1)$ is

1. $y=x{e}^{cx}$
2. $y+x{e}^{cx}=0$
3. $y+e^x=0$
4. $Noneofthese$

Q. Find the derivative of $x^2-1$ at $x=10$.