Question

x dy/dx = y+2xe^-y/x​

Answer 1

Answer:

x dy/dx = y+2xe^-y/xx dy/dx = y+2xe^-y/xxub can go ggixd going to ht

Answer 2

Step-by-step explanation:

xdy/dx=y+2e^-y/x

or,

dy/dx=(y+2e^-y/x) /x

let y=vx

so, dy/dx=v+xdv/dx

Now,

v+xdv/dx={vx+2e^-(vx/x) }

xdv/dx={vx+2e^-v}-v

xdv/dx=vx+2e^-v-vx

dv/dx=(2e^-v) /x

dv/2e^-v=dx/x

e^vdv/2=dx/x

integrating both side

we get,

e^v=logx+logc

e^y/x=logx+logc