1.

The general solution of `(dy)/(dx)=2xe^(x^(2)-y)` isA. `e^(x^(2)-y)=C`B. `e^(-y)+e^(x^(2))=C`C. `e^(y)+e^(x^(2))+C`D. `e^(x^(2)+y)=C`

Answer» Given that, `" "(dy)/(dx)=2xe^(x^(2)-y)=2xe^(x^(2))*e^(-y)`
`rArr" "e^(y)(dy)/(dx)=2xe^(x^(2))`
`rArr" "e^(y)dy=2xe^(x^(2))dx`
On integrating both sides, we get
`" "inte^(y)dy=2intxe^(x^(2))dx`
Put `x^(2)=t` in RHS integral, we get
`" "2xdx=dt`
`" "inte^(y)dy=inte^(t)dt`
`rArr" "e^(y)=e^(t)+C`
`rArr" "e^(y)=e^(x^(2))+C`


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