अवकल समीकरण `ye^((x)/(y))dx=(xe^((x)/(y))+y^(2))dy(yne0)` का हल ज्ञात कीजिए।

Explanation

दिया गया अवकल समीकरण `ye^((x)/(y))dx=(xe^((x)/(y))+y^(2))dy` है|
`implies e^((x)/(y))(dx)/(dy)=(x)/(y)e^((x)/(y))+y`
`implies e^((x)/(y))(dx)/(dy)-(x)/(y)e^((x)/(y))=y" ....(1)"`
मान लीजिए `(x)/(y)=vimpliesx=vyimplies(dx)/(dy)=v+y(dv)/(dx)`
समीकरण (1) से, `e^(v)(v+y(dv)/(dy))-ve^(v)=y`
`implies e^(v)y(dv)/(dy)=yimpliese^(v)(dv)/(dy)=1impliese^(v)dv=dy`
समाकलन करने पर,
`inte^(v)dv=int1dyimpliese^(v)=y+Cimplies e^((x)/(y))=y+C`