Question

The given differential equation point
is exact."
(x² + y2 + 2x)dx + 2ydy = 0)
O True
оо
False​

Answer 1

Answer:

x

2

+y

2

+2x)dx+2ydy=0⇒2y

dx

dy

+y

2

=−x(x+2)

Substitute v=y

2

⇒dv=2ydy

∴

dx

dv

+v=−x(x+2) ...(1)

Here P=1⇒∫Pdx=∫dx=x

∴I.F.=e

x

Multiplying (1) by I.F. we get

2ye

x

dx

dy

+y

2

e

x

=−x(x+2)e

x

Integrating both sides w.r.t x we get

v=−x

2

+ce

−x

⇒e

x

(x

2

+y

2

)=c