Question

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

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

Answer 1

The Correct Option is C

The correct option is(C): \(\frac{d^2y}{dx^2}-x^2\frac{dy}{dx}+xy=0\)

The given equation of curve is y=x.

Differentiating with respect to x,we get:

\(\frac{dy}{dx}\)=1...(1)

Again, differentiating with respect to x,we get:

\(\frac{d^2y}{dx^2}=0\)...(2)

Now, on substituting the values of y, \(\frac{d^2y}{dx^2}\),and \(\frac{dy}{dx}\) from equation (1) and (2) in each of

the given alternatives, we find that only the differential equation given in alternative C is correct.

\(\frac{d^2y}{dx^2}-x^2\frac{dy}{dx}+xy=0-x^2.1+x.x\)

\(=-x^2+x^2\)

=0

Hence,the correct answer is C.