Question

Which of the following equation is a linear differential equation of order $3$ ?

[Note: The original question asks for linear equation, but it should be linear differential equation]

• A. $\frac{d^{3}y}{d{x}^3}+\frac{d^{2}y}{d{x}^2}\frac{dy}{dx}+y=x$
• B. $\frac{d^{3}y}{d{x}^3}+\frac{d^{2}y}{d{x}^2}+y^2=x^2$
• C. $x\frac{d^{3}y}{d{x}^3}+\frac{d^{2}y}{d{x}^2}=e^x$
• D. $\frac{d^{2}y}{d{x}^2}+\frac{dy}{dx}=\log x$

Answer 1

Answer: (A)

$\frac{d^{3}y}{d{x}^3}+\frac{d^{2}y}{d{x}^2}\frac{dy}{dx}+y=x$

Linear equation is an equation between two variables that gives a straight line and order of linear equation is highest order derivative in linear equation.

Since, in option A equation is linear equation in which highest order is $3$.

$\therefore$ option A is correct.