M L Aggarwal Solutions for Chapter: Differential Equations, Exercise 1: EXERCISE

Determine the order and the degree (when defined) of differential equation, $3x\frac{dy}{dx}+\frac{5}{{\displaystyle \frac{dy}{dx}}}=y^3$.

Determine the order and the degree (when defined) of differential equation, $y=x\frac{dy}{dx}+a\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}$.

Determine the order and the degree (when defined) of  differential equation, $y^{\text{'}\text{'}}+{\left(y^{\text{'}}\right)}^2+2y=0$.

Determine the order and the degree (when defined) of differential equation, $y^{\text{'}\text{'}}+2y^{\text{'}}+\sin y=0$.

Determine the order and the degree (when defined) of differential equation, ${\left(y^{\text{'}\text{'}\text{'}}\right)}^2+{\left(y^{\text{'}\text{'}}\right)}^3+{\left(y^{\text{'}}\right)}^4+y^5=0$.

Determine the order and the degree (when defined) of differential equation, $y=px+\sqrt{a^2{p}^2+b^2}$ Where $p=\frac{dy}{dx}$.

Write the sum of the order and the degree of the differential equation: ${\left(\frac{d^{2}y}{d{x}^2}\right)}^2-{\left(\frac{dy}{dx}\right)}^3=y^3$.

Find the product of the order and degree of the differential equation, $x{\left(\frac{d^{2}y}{d{x}^2}\right)}^2+{\left(\frac{dy}{dx}\right)}^2+y^2=0$.