Observe the following statement .
I . If `dy + 2xy dx = 2e^(-x^(2))dx , ` then ` ye^(x^(2)) = 2x + C`
II. If ` ye^(x^(2)) - 2x = C , "then" dx = (2e^(-x^(2))) - 2xy )dy `
Which is/are correct statemant ?

Options

A. Both I and II are true
B. Neither I nor II is true
C. I is true II is false
D. I is flse , II is true

Answer

c

Explanation

` (dy)/(dx) +2xy = 2e^(-x^(2))`
This is linera differential equation
` :. IF = e^(int 2x dx ) = e^(x^(2))`
` :. "General solutin is "`
` ye^(x^(2)) * 2 x =e^(x^(2)) dx +C`
` rArr ye^(x^(2)) * 2x +e^(x^(2)) * (dy)/(dx) -2 =0`
` rArr e^(x^(2)) * (dy)/(dx)= 2 - 2xy e^(x^(2))`
` rArr (dy)/(dx) = 2e^(-x^(2))- 2xy`
Hence , I is true II is false