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Question
If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then
Options
m = 3, n = 3
m = 3, n = 2
m = 3, n = 5
m = 3, n = 1
MCQ
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Solution
m = 3, n = 2
We have,
\[ \left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\]
\[ \Rightarrow y_3 \left( y_2 \right)^5 + 4 \left( y_2 \right)^3 + \left( y_3 \right)^2 = y_3 \left( x^2 - 1 \right)\]
\[\text{ The highest order derivative is }y_3\text{ and its highest exponent in this equation is 2.}\]
Therefore, order is 3 and degree is 2.
Hence, m = 3, n = 2
\[ \left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\]
\[ \Rightarrow y_3 \left( y_2 \right)^5 + 4 \left( y_2 \right)^3 + \left( y_3 \right)^2 = y_3 \left( x^2 - 1 \right)\]
\[\text{ The highest order derivative is }y_3\text{ and its highest exponent in this equation is 2.}\]
Therefore, order is 3 and degree is 2.
Hence, m = 3, n = 2
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