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The order and degree of the following differential equation -d/dx { (dy/dx)4 } = 0 |
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Answer» Given : \(\frac{d}{dx}\bigg[\Big(\frac{dy}{dx}\Big)^4\bigg]\)=0 By chain rule , \(\implies\)\(4\Big(\frac{dy}{dx}\Big)^3\Big(\frac{d^2y}{dx^2}\Big)\)=0 Order :order of highest derivative order=2 Degree: degree of derivative of highest order Degree=1 By using chain rule to evaluate the derivative on the left hand side, we get: \(\frac{d}{dx} {(\frac{dy}{dx})^4} = 0\) ⇒ 4 \((\frac{dy}{dx})^3 \frac{d^2y}{dx^2} = 0\) The order of this differential equation is 2 because the highest order derivative appearing in the equation is second order. The degree is the power of this highest order derivative. In this case degree is 1. |
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