Question

# $\frac{{d}^{3}y}{d{x}^{3}}+\frac{{d}^{2}y}{d{x}^{2}}+\frac{dy}{dx}+y\mathrm{sin}y=0$

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Solution

## $\frac{{d}^{3}y}{d{x}^{3}}+\frac{{d}^{2}y}{d{x}^{2}}+\frac{dy}{dx}+y\mathrm{sin}y=0$ In this differential equation, the order of the highest order derivative is 3 and its power is 1. So, the order of the differential equation is 3 and its degree is 1. It is a non-linear differential equation, as the exponent of the dependent variable is not equal to 1 (by expanding $y.\mathrm{sin}y$). Disclaimer: The answer given in the book has some error. The solution here is created according to the question given in the book.

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