d^2y/dx^2=[y+dy/dx]^3/2. find the order AND degree of the D.E.
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We need to find the order and degree of the differential equation
dx
2
d
2
y
=
y+(
dx
dy
)
2
Consider
dx
2
d
2
y
=
y+(
dx
dy
)
2
⇒
dx
2
d
2
y
={y+(
dx
dy
)
2
}
1/2
⇒[
dx
2
d
2
y
]
2
=y+(
dx
dy
)
2
We know that, the order of a differential equation is the order of the highest order derivative present in the equation and the degree of a differential equation is the power of the highest order derivative in the equation.
Here the highest order derivative is 2 and its power is 2.
Thus order is 2 and power is 2.
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