R D Sharma Solutions for Chapter: Differential Equations, Exercise 12: VERY SHORT ANSWER QUESTIONS (VSAQs)

If $\sin x$ is an integrating factor of the differential equation $\frac{dy}{dx}+Py=Q$, then write the value of $P$.

Write the degree of the differential equation ${\left(\frac{dy}{dx}\right)}^4+3x\frac{d^{2}y}{d{x}^2}=0$.

Write the degree of the differential equation $x{\left(\frac{d^{2}y}{d{x}^2}\right)}^3+y{\left(\frac{dy}{dx}\right)}^4+x^3=0$

Write the degree of the differential equation $x^3{\left(\frac{d^{2}y}{d{x}^2}\right)}^2+x{\left(\frac{dy}{dx}\right)}^4=0$

Write the degree of the differential equation ${\left(1+\frac{dy}{dx}\right)}^3={\left(\frac{d^{2}y}{d{x}^2}\right)}^2$

How many arbitrary constants are there in the general solution of the differential equation of order $3$.

Write the order of the differential equation representing the family of curves $y=ax+a^3$

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