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Q18.    The general solution of the differential equation e^x dy + (y e^x + 2x) dx = 0 is

            (A)    xe^y + x^2 = C

            (B)    xe^y + y^2 = C

            (C)    ye^x + x^2 = C

            (D)    ye^y + x^2 = C

Answers (1)

best_answer

Given equation is
e^x dy + (y e^x + 2x) dx = 0
we can rewrite it as
\frac{dy}{dx}+y=-2xe^{-x}
It is \frac{dy}{dx}+py=Q type of equation where p = 1 \ and \ Q = -2xe^{-x}
Now,
I.F. = e^{\int p dx }= e^{\int 1dx}= e^x
Now, the general solution is
y(I.F.) = \int (Q\times I.F.)dx+C
y(e^x) = \int (-2xe^{-x}\times e^x)dx+C\\ ye^x= \int -2xdx + C\\ ye^x=- x^2 + C\\ ye^x+x^2 = C
Therefore, (C) is the correct answer

Posted by

Gautam harsolia

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