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# The degree of the differential equation $1+\bigg[\bigg(\large\frac{dy}{dx}\bigg)^2\bigg]^{\large\frac{3}{2}}=\frac{d^2y}{dx^2}$ is:$(A)\;4\quad(B)\;\frac{3}{2}\quad(C)\;not\;defined\quad(D)\;2$

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## 1 Answer

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Toolbox:
• The power of the highest order differential coefficient determines the degree of the equation.
$1+\bigg[\bigg(\large\frac{dy}{dx}\bigg)^2\bigg]^{\large\frac{3}{2}}=\frac{d^2y}{dx^2}$
To find the degree of the differential equation
Let us express this as a polynomial in derivative.
Let us square it on both sides
$\bigg[1+\bigg(\large\frac{dy}{dx}\bigg)^2\bigg]^3=\bigg(\large\frac{d^2y}{dx^2}\bigg)^2$
Clearly the power of the highest order differential coefficient is $2$. So its degree is $2$
Hence the correct option is $D$
answered May 14, 2013 by

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