A. The degree of differential equation $\frac{d^2 y}{d x^2}+\sin \left(\frac{d y}{d x}\right)=0$ is 2.
B. The degree of differential equation $\frac{d}{d x}\left(\frac{d y}{d x}\right)+\left(\frac{d y}{d x}\right)^3+\sin x=0$ is 1.
C. The order of differential equation $2 x^2 \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+y=0$ is 2.
D. The number of arbitrary constants in a particular solution of a differential equation of third order are 3.
E. The integrating factor of the differential equation $\frac{d y}{d x}-y=\cos x$ is $e^{-x}$.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → B, C, E only
(A) False, as $\frac{dy}{dx}$ is in $\sin e$ term ⇒ degree not defined
(B) True
(C) True
(D) False, No. of arbitrary constants always 0 in particular solution
(E) True