Which of the following differential equations has the same order … - Vidyadip

MCQ

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

A
$\frac{{{d^4}y}}{{d{x^4}}} + 8{\rm{ }}{\left( {\frac{{dy}}{{dx}}} \right)^6} + 5y = {e^x}$
B
$5{\rm{ }}{\left( {\frac{{{d^3}y}}{{d{x^3}}}} \right)^4} + 8{\rm{ }}{\left( {1 + \frac{{dy}}{{dx}}} \right)^2} + 5y = {x^8}$
✓
${\left[ {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^3}} \right]^{2/3}} = 4\frac{{{d^3}y}}{{d{x^3}}}$
D
$y = {x^2}\frac{{dy}}{{dx}} + \sqrt {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} $

✓

Answer

Correct option: C.

${\left[ {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^3}} \right]^{2/3}} = 4\frac{{{d^3}y}}{{d{x^3}}}$

c
(c) Option $(a)$ has order $= 4$, degree $ = 1$

Option $(b)$ has order $= 3$, degree $ = 4$

Option $(c)$ has order $= 3$, degree $ = 3$ (taking cube)

Option $(d)$ has order $ =1$, degree $ = 2$ (squaring).

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