Question

solve (ORDINARY DIFFERENTIAL)
dy/dx + y/x = y^2sinx​

Answer 1

Answer:

dy

+xy=y

2

e

2

x

2

.sinx⇒

y

2

1

dx

dy

+

y

x

=e

2

x

2

.sinx

Substitute −

y

1

=v⇒

y

2

1

dy=dv

∴

dx

dv

−vx=e

2

x

2

.sinx ...(1)

Here P=−x⇒∫Pdx=−∫xdx=

2

−x

2

∴I.F.=e

2

−x

2

Multiplying (1) by I.F. we get

e

2

−x

2

dx

dv

−vxe

2

−x

2

=sinx

Integrating both sides we get

e

2

−x

2

v=∫sinxdx+c=−cosx+c⇒e

2

−x

2

=y(c+cosx)

Step-by-step explanation:

hope it will help you