The particular solution of the differential equation $$\left(1+e^{2 x}\right) d y+e^x\left(1+y^2\right) d x=0$$ at $$x=0$$ and y = 1 is

The order and degree of the differential equation $$\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$$ are respectively.

A population P grew at the rate given by the equation $$\frac{dP}{dt}=0.5P$$, then the population will become double in

The differential equation of all parabolas whose axis is $$y$$-axis, is