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  • Which of the following is a second order differential equation? A. (y’)2 + x = y2 B. y’y’’ + y = sinx C. y’’’+(y’’)2+y=0 D. y’ = y2

Which of the following is a second order differential equation?
\\A. \left(y^{\prime}\right)^{2}+x=y^{2} \\B. y^{\prime} y^{\prime \prime}+y=\sin x \\C. y^{\prime \prime \prime}+\left(y^{\prime \prime}\right)^{2}+y=0 \\D. y^{\prime}=y^{2}

Answers (1)

Order is defined as the number which defines the highest derivative in a differential equation

Second order means the order should be 2 which means the highest

derivative in the equation should be \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}$ or y Let's examine each of the option given
A. \left(y^{\prime}\right)^{2}+x=y^{2}$
The highest order derivative is y^{\prime}$ is in first order.
B. y^{\prime} y^{\prime \prime}+y=\sin x$
The highest order derivative is y^{\prime \prime}$ is in second order
C. y^{\prime \prime \prime}+\left(y^{\prime \prime}\right)^{2}+y=0$
The highest order derivative is y^{\prime \prime \prime}$ is in third order
D. y^{\prime}=y^{2}$
The highest order derivative is y ' is in first order

Option B is correct.

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