Embibe Experts Solutions for Chapter: Differential Equations, Exercise 2: EXERCISE-2

The differential equation $2xydy=\left(x^2+y^2+1\right)dx$ determines

If $f^{\text{'}\text{'}}\left(x\right)+f^{\text{'}}\left(x\right)+f^2\left(x\right)=x^2$ be the differential equation of a curve and let $P$ be the point of maxima then number of tangents which can be drawn from point $P$ to $x^2-y^2=a^2,a\ne 0$ is -

The solution of $x^{2}dy-y^{2}dx+x{y}^2(x-y)dy=0$ is -

The orthogonal trajectories of the system of curves ${\left(\frac{dy}{dx}\right)}^2=\frac{4}{x}$ are -

If $x\frac{dy}{dx}=y\left(\log y-\log x+1\right)$, then the solution of the equation is -

Solutions of the differential equation $x^2{\left(\frac{dy}{dx}\right)}^2+xy\left(\frac{dy}{dx}\right)-6y^2=0$

The solution the differential equation ${\left(\frac{dy}{dx}\right)}^2-\frac{dy}{dx}\left(e^x+e^{-x}\right)+1=0$ is are -

A normal is drawn at a point $P(x,y)$ of a curve. It meets the $x$-axis and the $y$-axis in point $A$ and $B,$ respectively, such that $\frac{1}{OA}+\frac{1}{OB}=1,$ where $O$ is the origin, the equation of such a curve is a circle which passes through $\left(5,4\right)$ and has -