Question

Which one of the following differential equations is not linear?

• A. $\frac{d^{2}y}{d{x}^2}+4y=0$
• B. $x\frac{dy}{dx}+y=x^3$
• C. $(x-y{)}^2\frac{dy}{dx}=9$
• D. ${\cos }^{2}x\frac{dy}{dx}+y=\tan x$

Answer 1

Answer: (A)

$\frac{d^{2}y}{d{x}^2}+4y=0$

In a differential equation, when the variables and their derivatives are only multiplied by constants, then the equation is linear.

Except first all other options are non linear equations as in every equation, they are multiplied by other variables.

Hence, only A is not a linear differential equation.