Statement 1: The degrees of the differential equations $\frac{d y}{d x}+y^2=x$ and $\frac{d^2 y}{d…
Statement 1: The degrees of the differential equations $\frac{d y}{d x}+y^2=x$ and $\frac{d^2 y}{d x^2}+y=\sin x$ 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.
Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
Statement 1 is false, Statement 2 is true.
Statement 1 is true, Statement 2 is false.
Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1.
Solution
Statement-1
Given differential equations are $\frac{d y}{d x}+y^2=x$ and $\frac{d^2 y}{d x^2}+y=\sin x$
Their degrees are 1 .
Both have equal degree.
Also, Statement $-2$ is the correct explanation for Statement - 1.