Which of the following differential equations has the same order and degree-

Mathematics · JEE Main · NTA Exams — Differential Equations

1. \(\frac{d^{4} y}{d x^{4}}\)+ 8 \(\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{6}\)+ 5y = e^x
2. 5 \(\left(\frac{d^{3} y}{d x^{3}}\right)^{4}\)+ 8 \(\left(1+\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}\)+ 5y = x⁸
3. \[\left[1+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{3}\right]^{2 / 3}=4 \frac{\mathrm{~d}^{3} \mathrm{y}}{\mathrm{dx}^{3}}\]
4. y = x² \(\frac{\mathrm{dy}}{\mathrm{dx}}+\sqrt{1+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}}\)

Answer

(C) [1+ ( dy dx )^ 3 ]^ 2 / 3 =4 ~d ^ 3 y dx ^ 3

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