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

Find the order and degree of the differential equation ${\left[\frac{d^{2}y}{d{x}^2}-{\left(\frac{dy}{dx}\right)}^3\right]}^{\frac{6}{5}}=6y$.

Obtain the differential equation which corresponds to the rectangular hyperbolas having the coordinate axes as asymptotes.

Obtain the differential equation which corresponds to the ellipses with centers at the origin and having coordinate axes as axes.

Form the differential equation the family of curves $y=a{e}^{3x}+b{e}^{4x}$ where $a$ and $b$ are the parameters.

Form the differential equation of the following family of curves where parameters are given in bracket: $y=a{x}^2+bx$; $(a,b)$

Form the differential equation of the following family of curves where parameters are given in bracket: $a{x}^2+b{y}^2=1$; $(a,b)$

Form the differential equation of the following family of curves where parameters are given in bracket: $xy=a{x}^2+b/x$; $(a,b)$

Obtain the differential equation which corresponds to the family of circles which touch the $Y$-axis at the origin