Question

for x, y belongs to R if (x-2) +(y-1) /=2+x/ then y equals​

Answer 1

Answer:

x∫

1

x

y(t)dt=x∫

1

x

ty(t)dt+∫

1

x

ty(t)dt

differentiate w.r. to x.

∫

1

x

y(t)dt+x[y(x)−y(1)]=∫

1

x

ty(t)dt+x[xy(x)−y(1)]+xy(x)−y(1)

∫

1

x

y(t)dt=∫

1

x

ty(t)dt+x

2

y(x)−y(1)

diff. again w.r to x

y(x)−y(1)=xy(x)−y(1)+2xy(x)+x

2

y

′

(x)

(1−3x)y(x)=x

2

y

′

(x)

y(x)

y

′

(x)

=

x

2

1−3x

y

1

dx

dy

=

x

2

1−3x

⇒ln y=−

xx1

−3ln x

ln(yx

3

)=−

x

1

+lnc

yx

3

=ce

−

x

1

y=c

x

3

e

−

x

1

or y=

x

3

ce

−

x

1