differential equation for
What is the
y2 = 4a (x - a) ?
Answers
Answered by
0
Answer:
Given, y
2
=4a(x+a)
Differentiating both side w.r.t. x, we get,
dx
d
y
2
=
dx
d
4a(x+a)
2y
dx
dy
=
dx
d
4ax+
dx
d
4a
2
2y
dx
dy
=4a+0
dx
dy
=
y
2a
Now,
y{1−(
dx
dy
)
2
}=2x
dx
dy
L.H.S=y{1−(
dx
dy
)
2
}
Put the value of
dx
dy
=
y
2a
=y{1−(
y
2a
)
2
}
=y{1−(
y
2
4a
2
)}
=y(
y
2
y
2
−4a
2
)
Simplifying
=(
y
y
2
−4a
2
)
Given, y
2
=4a(x+a)
=(
4a(x+a)
4a(x+a)−4a
2
)
=(
4a(x+a)
4ax+4a
2
−4a
2
)
=(
4a(x+a)
4ax
)
=2x(
4a(x+a)
2a
)
=2x(
y
2a
)
=2x
dx
dy
=R.H.S
∴y
2
=4a(x+a) is a solution for the differential equation y{1−(
dx
dy
)
2
}=2x
dx
dy
Similar questions