The differential equation of the family of circles touching $$y$$-axis at the origin is

The general solution of the differential equation. $$\left(\frac{y}{x}\right) \cos \left(\frac{y}{x}\right) d x-\left[\left(\frac{x}{y}\right) \sin \left(\frac{y}{x}\right)+\cos \left(\frac{y}{x}\right)\right] d y=0$$ is

If the half life period of a substance is 5 years, then the total amount of the substance left after 15 years, when initial amount is 64 gms is

If $$m$$ is order and $$n$$ is degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\frac{d^2 y}{d x^2}\right)}{\left(\frac{d^3 y}{d x^3}\right)}+\left(\frac{d^3 y}{d x^3}\right)=x^2$$ then