Which of the following statements are true ?
A. Degree of the differential equation $\frac{d^2y}{dx^2}+y =1$ is 2.
B. Number of arbitrary constants in the particular solution the differential equation of order 4 are 4.
C. $y^2=a(b^2-x^2)$ will be the general solution of a differential equation of order 2; where a and b are two arbitrary constants.
D. $f(x, y) =\frac{2x-y}{x+3y }$ is a homogeneous function of degree 1.
E. Integrating factor of $x\frac{dy}{dx}-y=2x^2$ is $\frac{1}{x}$.
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → C and E only
(A) false degree can't be found as still 1 constant is remaining in eq.
(B) false, no arbitrary constant exists in particular solution
(C) True
(D) false, it is homogeneous function of degree 0.
(E) $I. F.=e^{∫-\frac{1}{x}dx}=\frac{1}{x}$ (true)