Order of a differential equation is the highest power of any derivative appearing in the differential equation

Q. Order of a differential equation is the highest power of any derivative appearing in the differential equation

Q. Assertion :The degree of the differential equation, $\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2+\sin \left(\frac{dy}{dx}\right)+1=0$ is 1 Reason: By the degree of a differential equation, when it is a polynomial equation in derivatives, we mean the highest power (positive integral index) of the highest order derivative involved in the given differential equation.

Q. Assertion :The order of the differential equation whose solution is $y=c_1{e}^{2x+c_2}+c_3{e}^{2x+c_4}$ is 4. Reason: Order of the differential equation is the order of the highest order derivative occurring in the differential equation.

Q. The order and power of differential equation
$\frac{d^{2}y}{d{x}^2}+y\frac{dy}{dx}+\int ydx=\sin x$ is

Q. Assertion :The differential equation of all circles in a plane is of order $3$ Reason: Only one circle can be drawn through any three points in a plane