Question

differential equation for
What is the
y2 = 4a (x - a) ?​

Answer 1

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