Differential Equations

What is the degree of the differential equation of all circles touching both the coordinate axes in the first quadrant?

The degree and order respectively of the differential equation $\frac{d y}{d x}=\frac{1}{x+y+1}$ are

The differential equation of the curve $y=\sin x$ is

What is the degree of the differential equation $\frac{d^3 y}{d x^3}+\left(\frac{d y}{d x}\right)^2-x^2\left(\frac{d^4 y}{d x^4}\right)=0$ ?

Which one of the following differential equations has a periodic solution?

A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decays in 100 years, then what is the decay constant (proportionality constant)?

What is the degree of the differential equation $\left(\frac{d^3 y}{d x^3}\right)^{3 / 2}=\left(\frac{d^2 y}{d x^2}\right)^2 ?$

The general solution of $\frac{d y}{d x}=\frac{a x+h}{b y+k}$ represents a circle only when

Passage: Consider the differential equation $e^{x+y}\dfrac{dy}{dx}=e^{x-y}$. Question: What is the solution of the differential equation with $y(0)=0$ ?

A parabola pases through $(1,2)$ and satisfies the differential equation $\frac{d y}{d x}=\frac{2 y}{x}, x \gt 0, y \gt 0$. What is the directrix of the parabola?

The order and degree of the differential equation $k \frac{d y}{d x}=\int\left[1+\left(\frac{d y}{d x}\right)^2\right]^{\frac{2}{3}} d x$ are respectively

What is the differential equation of the family of parabolas having vertex at origin and axis along positive $y$-axis ?