Embibe Experts Solutions for Chapter: Differential Equation, Exercise 1: AMU-AT (B.Tech.) 2017

A curve having the condition that the slope of tangent at some point is two times the slope of the straight line joining the same point to the origin of co-ordinates, is a/an

If $a$ is an arbitrary constant, then solution of the differential equation $\frac{dy}{dx}+\sqrt{\frac{1-y^2}{1-x^2}}=0$ is

The solution of the equation $x^2\frac{d^{2}y}{d{x}^2}=\log x$ when $x=1, y=0$ and $\frac{dy}{dx}=-1$ is

The solution of the differential equation $\frac{dy}{dx}=\frac{2xy-y^2}{2xy-x^2},$ is

$y=a\cos \left(\log x\right)+b\sin \left(\log x\right)$ is a solutión of the differential equation

The integrating factor of the differential equation $\left(x\log x\right)\frac{dy}{dx}+y=2\log x$ is

The function $y=c_1\cos x+c_2\sin x$ is a solution of the $DE,$ where $c_1$ and $c_2$ are real numbers

The general solution of differential equation $\frac{dy}{dx}+2xy=2e^{-x^2}$ is