Question

xdy - ydx = (x² + y²)(xdx+ydy) solve differential equation
step by step with explaination​

Answer 1

Answer:

xdy−ydx=(x

2

+y

2

)dx⇒x

dx

dy

−y=x

2

+y

2

Substitute y=vx⇒

dx

dy

=v+x

dx

dv

∴x(x

dx

dv

+v)−xv=x

2

+x

2

v

2

⇒

dx

dv

=v

2

+1⇒

v

2

+1

1

dx

dv

=1

Integrating both sides

∫

v

2

+1

1

dx

dv

dx=∫dx

⇒tan

−1

v=x+c⇒v=tan(x+c)⇒y=xtan(x+c)