If the order and degree of the differential equation \( y+\displaystyle\frac{dy}{dx}=\int y\,dx \) are m and n respectively, then (m - n) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
The equation contains an integral of y, which is removed by differentiating both sides with respect to x, using \( \frac{d}{dx}\int y\,dx=y \).
\( \displaystyle \frac{dy}{dx}+\frac{d^2y}{dx^2}=y \)
This is a polynomial in the derivatives. The highest derivative is \( \frac{d^2y}{dx^2} \), with power 1.
\( \displaystyle m=2,\ n=1 \)
\( \displaystyle m-n=2-1=1 \)
Why the other options are incorrect
Option (1) 0 — Incorrect. m − n = 0 would need the order and the degree to be equal; here the order is 2 and the degree is 1.
Option (3) −1 — Incorrect. −1 is n − m, with the order and the degree interchanged.
Option (4) Not defined — Incorrect. The integral is removed by differentiating once, and the resulting equation is a polynomial in its derivatives, so both the order and the degree are defined.