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The order and degree of the differential equation $\left[1+\frac{1}{\left(\frac{d y}{d x}\right)^{2}}\right]^{\frac{5}{3}}=5 \frac{d^{2} y}{d x^{2}}$ are
respectively
Options:
respectively
Solution:
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Verified Answer
The correct answer is:
2,3
(D)
Raising both sides of differential equation to degree 3 , we get
$\begin{array}{l}
{\left[1+\frac{1}{\left(\frac{d y}{d x}\right)^{2}}\right]^{5}=125\left(\frac{d^{2} y}{d x^{2}}\right)^{3}} \\
{\left[\left(\frac{d y}{d x}\right)^{2}+1\right]^{5}=125 \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{3}\left[\left(\frac{d y}{d x}\right)^{2}\right]^{5}}
\end{array}$
$\therefore$ Its order is 2 and degree is $3 .$
Raising both sides of differential equation to degree 3 , we get
$\begin{array}{l}
{\left[1+\frac{1}{\left(\frac{d y}{d x}\right)^{2}}\right]^{5}=125\left(\frac{d^{2} y}{d x^{2}}\right)^{3}} \\
{\left[\left(\frac{d y}{d x}\right)^{2}+1\right]^{5}=125 \cdot\left(\frac{d^{2} y}{d x^{2}}\right)^{3}\left[\left(\frac{d y}{d x}\right)^{2}\right]^{5}}
\end{array}$
$\therefore$ Its order is 2 and degree is $3 .$
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