Saved Bookmarks
| 1. |
What is the degree of the differential equation \(\rm y = x \dfrac{dy}{dx}+\left(\dfrac{dy}{dx}\right)^{-2} \ ?\)1. 12. 33. -24. Degree does not exist. |
|
Answer» Correct Answer - Option 2 : 3 Concept: Order: The order of a differential equation is the order of the highest derivative appearing in it. Degree: The degree of a differential equation is the power of the highest derivative occurring in it, after the Equation has been expressed in a form free from radicals as far as the derivatives are concerned. Calculation: Given: \(\rm y = x \frac{dy}{dx}+\left(\frac{dy}{dx}\right)^{-2} \\ \rm y = x\frac{dy}{dx}+\frac{1}{(\frac{dy}{dx})^2} \\ y(\frac{dy}{dx} )^2= x(\frac{dy}{dx})^3 + 1\) For the given differential equation the highest order derivative is 1. Now, the power of the highest order derivative is 3. We know that the degree of a differential equation is the power of the highest derivative. Hence, the degree of the differential equation is 3. |
|