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 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 $\frac{dy}{dx}=e^{x-y}+x^2{e}^{-y}$ will be

If $y=y\left(x\right), y\in \left[0,\frac{\pi }{2}\right)$ is the solution of the differential equation $\sec y\frac{dy}{dx}-\sin \left(x+y\right)-\sin \left(x-y\right)=0,$ with $y\left(0\right)=0$, then $5y^{\text{'}}\left(\frac{\pi }{2}\right)$ is equal to _____.

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

The solution of the differential equation $\frac{dy}{dx}+\frac{\sin 2y}{x}=x^3{\cos }^{2}y,$ is (where $C$ is a constant of integration)