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

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

What is the order of the differential equation whose solution is $y=a\cos x+b\sin x+c{e}^{-x}+d$ where $a, b, c$ and $d$ are arbitrary constants?

The equation of the curve passing through the point $(-1,-2)$ which satisfies $\frac{dy}{dx}=-x^2-\frac{1}{x^3}$ is

Let $y=f\left(x\right)$ be a curve which passes through $\left(3,1\right)$ and is such that normal at any point on it passes through $\left(1,1\right)$. Then, $y=f\left(x\right)$ describes

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

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

$A$ & $B$ 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?