Question

Which of the following differential equations has y = x as one of its particular solution?

• A. $\frac{d^{2}y}{d{x}^2}-x^2\frac{dy}{dx}+xy=x$
• B. $\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}+xy=x$
• C. $\frac{d^{2}y}{d{x}^2}-x^2\frac{dy}{dx}+xy=0$
• D. $\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}+xy=0$

Answer 1

Answer: (C)

$\frac{d^{2}y}{d{x}^2}-x^2\frac{dy}{dx}+xy=0$

$y=x\frac{dy}{dx}=1\frac{d^{2}y}{d{x}^2}=0$
Now putting these values in given options then we will find that
Option C is correct
$\frac{d^{2}y}{d{x}^2}-x^2\frac{dy}{dx}+xy=0$