Embibe Experts Solutions for Chapter: Differential Equation, Exercise 1: KCET (UG) 2021

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

Solution of Differential Equation $xdy-ydx=0$ represents

The number of solutions of $\frac{dy}{dx}=\frac{y+1}{x-1}$, when $y\left(2\right)=1$, is

The general solution of the differential equation $x^{2}dy-2xy\mathrm{d}x=x^4\cos x\mathrm{d}x$ is

The solution of the differential equation $x\left(\frac{dy}{dx}\right)-y=3$ represents a family of

The integrating factor of $\left(\frac{dy}{dx}\right)+y=\frac{\left(1+y\right)}{x}$ is

The curve passing through the point $(1,2)$ given that the slope of the tangent at any point $(x,y)$ is $\frac{2x}{y}$ represents

The equation of the curve passing through the point $\left(1, 1\right)$ such that the slope of the tangent at any point $\left(x, y\right)$ is equal to the product of its co-ordinates is