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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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The order and degree of the differential equation $\bigg(\frac{d^3y}{dx^3}\bigg)^2+3\frac{d^2y}{dx^2}+2\bigg(\frac{dy}{dx}\bigg)^4=y^4$ are

\[(A)\;1,4\quad(B)\;3,4\quad(C)\;2,4\quad(D)\;3,2\]

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1 Answer

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Toolbox:
  • The order of a differeential equation is the highest order to which it belongs
  • The degree of a differential equation is the power of the highest order differential coefficient
Given equation is
$\bigg(\Large\frac{d^3y}{dx^3}\bigg)^2$$+3\Large\frac{d^2y}{dx^2}$$+2\Large\bigg(\frac{dy}{dx}\bigg)^4$$=y^4$
It is clearly that the highest order of eqauation is $\Large\frac{d^3y}{dx^3}$
Hence the order is $3$
The power of the highest order differential coefficient is $2$
Hence its degree is $2$
Clearly the above equation is a non-linear differential equation of order $3$ and degree $2$
Hence the correct option is $D$
answered May 20, 2013 by meena.p
 

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