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# Which of the following is a second order differential equation\begin{array}{1 1}(A)\;(y')^2+x=y^2 & (B)\;y' y''+y=\sin x\\(C)\;y'''+(y'')^2+y=0 & (D)\;y'=y^2\end{array}

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Toolbox:
• The highest order of the derivative of y determines the order of the differential equation.
The given equations are
$(A)\;(y')^2+x=y^2$
$(B)\;y' y''+y=\sin x$
$(C)\;y'''+(y'')^2+y=0$
$(D)\;y'=y^2$
In equation $A$ is $y'$ has order $1$
Hence it is a First order differential equation
In equation $B$ is $y'y''$ has order $2$
Hence it is a second order differential equation
In equation $C$ is $y'''$ has order $3$
Hence it is a Third order differential equation
In equation $D$ is $y'$ has order $1$
Hence it is a First order differential equation
Hence the correct option is $B$
answered May 16, 2013 by