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.
  1. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
  2. Statement 1 is false, Statement 2 is true.
  3. Statement 1 is true, Statement 2 is false.
  4. 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.

Asked in: JEE Main 2012 (12 May Online)

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