$$ \int_0^{\pi / 2} \sin ^4 \theta \cos ^3 \theta d \theta= $$

Statement I The differential equation corresponding to the family of circles having their centres on $Y$-axis and fixed radius $k$ is $\left(x^2-k^2\right)\left(\frac{d y}{d x}\right)^2+x^2=0$

Statement II The differential equation corresponding to the family of circles passing through the origin and having their centres on $X$-axis is $x^2-y^2+2 x y \frac{d y}{d x}=0$

Which of the above statements is (are) true?

If $m$ and $n$ are respectively the order and the degree of the differential equation representing the family of curves $y^2-5 a x-5 a^{3 / 2}=0(a>0$ is a parameter), then the value of $m-n$ is

The general solution of $\left(\left(1+x^2\right) y \sin x-2 x y\right) d x-\log y^{1+x^2} d y=0$ is