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Home  >>  CBSE XII  >>  Math  >>  Differential Equations
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$y=ae^{mx}+be^{-mx}$ satisfies which of the following differential equation?

\[(A)\;\frac{dy}{dx}+my=0 \quad (B)\;\frac{dy}{dx}-my=0\quad(C)\;\frac{d^2y}{dx^2}-m^2y=0 \quad (D)\;\frac{d^2y}{dx^2}+m^2y=0\]

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  • The general solution of a differential equation is a relation between dependent and independent variable having n arbitary constant.
  • The general solution may have more than one form but the arbitary constants must be the same in numbers
Given $y=ae^{mx}+be^{-mx}$
On differentiaiting w.r.t x we get
Again differentiating w.r.t. x we get
But $ae^{mx}+be^{-mx}=y$
Hence the correct option is $C$
answered May 21, 2013 by meena.p

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