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Shown below is a differential equation. \[ y= e ^{\sin \left(\frac{d^{3} y}{d x^{3}}\right)^{2}}+\left(\frac{d y}{d x}\right)^{4} \]Find the order and the degree of the given differential equation. Give reasons to support your answer. |
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Answer» The differential equation is y = esin\((\frac{d^3y}{dx^3})^2+(\frac{dy}{dx})^4\) Highest order derivative is \(\frac{d^3y}{dx^3}\) But differential equation is not a polynomial equation in derivative of y. ∴ Degree is not defined Order = Order of highest order derivative=3 Hence, order of differential equation is 3 but degree is not defined. |
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