Question

solve by bernoulli's equation xy(1+xy^2)dy/dx=1

Answer 1

Answer:

dx

dy

(x

2

y

3

+xy)=1

dx

dy

=

x

2

y

3

+xy

1

dy

dx

=x

2

y

3

+xy

dy

dx

−xy=x

2

y

3

x

2

1

dy

dx

−

x

y

=y

3

substitute

x

1

=u

dy

du

=−

x

2

1

dy

dx

−

dy

du

−uy=y

3

dy

du

+uy=−y

3

I.F=e

∫ydy

=e

2

y

2

u×e

2

y

2

=−∫y

3

e

2

y

2

dy

=−2(

2

y

2

−1)e

2

y

2

+c

=(2−y

2

)e

2

y

2

+c

⇒x(2−y

2

)+cxe

−

2

y

2

=1