Observe the following statements. I. IF $dy + 2xy\ dx = 2e^{- x^{2}}\ dx$, then $ye^{x^{2}} = 2x + c$ II.IF $ye^{x^{2}} - 2x = c$, then $dx = \left( 2e^{- x^{2}} - 2xy \right)dy$ Which is/are correct statements?

Question

Dr. Abubacker · Accepted Answer

(c)
I.$\frac{dy}{dx} + 2xy = 2e^{- x^{2}}$
$	herefore$ $IF = e^{\int_{}^{}{2x\ dx}} = e^{x^{2}}$
$	herefore$ Complete solution is
$ye^{x^{2}} = 2\int_{}^{}e^{- x^{2}}e^{x^{2}}dx + c$
$\Rightarrow$ $ye^{x^{2}} = 2x + c$
II. $ye^{x^{2}} - 2x = c$
$\Rightarrow$ $ye^{x^{2}}.2x + e^{x^{2}}.\frac{dy}{dx} - 2 = 0$
$\Rightarrow$ $e^{x^{2}}.\frac{dy}{dx} = 2 - 2xy\ e^{x^{2}}$
$\Rightarrow$ $\frac{dy}{dx} = 2e^{- x^{2}} - 2xy$
$	herefore$ I is true and II is false.

Q. Observe the following statements. I. IF $dy + 2xy\ dx = 2e^{- x^{2}}\ dx$, then $ye^{x^{2}} = 2x + c$ II.IF $ye^{x^{2}} - 2x = c$, then $dx = \left( 2e^{- x^{2}} - 2xy \right)dy$ Which is/are correct statements?

Explanation

Reviewed by Dr. Abubacker

Want more practice?