` (dy)/(dx) + 2xy = x`, given that `y =1` when ` x =0`

1.	` (dy)/(dx) + 2xy = x`, given that `y =1` when ` x =0`
Answer» Correct Answer - ` 2y = 1 +e ^(-x^(2)) ` `IF = e ^(int 2 x dx ) = e ^(x^(2)) ` `therefore y xx e ^( x ^(2)) = int x e ^( x ^(2)) dx = (1)/(2) int e ^(t) dt +C`, where ` x ^(2) = t ` `" " = (1)/(2) e ^(x ^(2)) +C`. ` therefore y = (1)/(2) + ( C)/( e ^( x ^(2))) ` Putting `y = 1 and x = 0`, we get `C = (1)/(2)`.

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