Embibe Experts Solutions for Chapter: Differential Equations, Exercise 1: Exercise 1

The general solution of the differential equation $\frac{dy}{dx}+\sin \left(\frac{x+y}{2}\right)=\sin \left(\frac{x-y}{2}\right)$

The equations of motion of a particle are given by$\frac{dx}{dt}=t\left(t+1\right), \frac{dy}{dt}=\frac{1}{t+1}$ where the particle is at$\left(x\left(t\right),y\left(t\right)\right)$ at time $t$. If the particle is at the origin at $t=0$, then

$A$ & $B$ are two separate reservoirs of water. Capacity of reservoir $A$ is double the capacity of reservoir $B$. Both the reservoirs are filled completely with water, their inlet are closed and then the water is released simultaneously from both the reservoirs. The rate of flow of water out of each reservoir at any instant of time is proportional to the quantity of water in the reservoir at that time. One hour after the water is released, the quantity of water in reservoir $A$ is $1.5$ times the quantity of water in reservoir $B$. After how many hours do both the reservoirs have the same quantity of water?

The order of the differential equation of all parabolas whose axis of symmetry along $x$-axis is -

The solution of the differential equation $\frac{dy}{dx}=e^{x-y}+x^2{e}^{-y}$ will be

The differential equation whose solution is $a{x}^2+b{y}^2=1$, where $a$ and $b$ are arbitrary constants, is of

The differential equation of the family of circles having centre on $Y$-axis and radius $4$ is

The solution of the differential equation $e^{\frac{dy}{dx}}=x+1$ when $y\left(0\right)=3$