Question

Statement 1 : The degrees of the differential equations $\frac{dy}{dx}+y^{2} = x$ and $\frac{d^{2}y}{dx^{2}} + y = sin\,x$ are equal.
Statement 2 : The degree of a differential equation, when it is a polynomial equation in derivatives, is the highest positive integral power of the highest order derivative involved in the differential equation, otherwise degree is not defined.

• A. Statement 1 is true, Statement 2 is true. Statement 2 is not a correct explanation of Statement 1.
• B. Statement 1 is felse, Statement 2 is true.
• C. Statement 1 is true, Statement 2 is false.
• D. Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.

Answer 1

Answer: (D)

Statement-1
Given differential equations are
$\frac{dy}{dx}+y^{2} = x$ and $\frac{d^{2}y}{dx^{2}} + y = sin\,x $
Their degrees are 1.
Both have equal degree.
Also, Statement - 2 is the correct explanation for Statement -1.