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  • The general solution of the differential equation y dx - x dy /y = 0 is (A) xy = C (B) x = Cy^2 (C) y = Cx (D) y = Cx^2

Q16.    The general solution of the differential equation \frac{ydx - xdy}{y} = 0is

            (A)    xy = C

            (B)    x = Cy^2

            (C)    y = Cx

            (D)    y = Cx^2

Answers (1)

best_answer

Given equation is
\frac{ydx - xdy}{y} = 0
we can rewrite it as 
dx = \frac{x}{y}dy\\ \frac{dy}{y}=\frac{dx}{x}
Integrate both the sides
we will get
\log |y| = \log |x| + C\\ \log \frac{y}{x} = C \\ \frac{y}{x} = e^C\\ \frac{y}{x} = C\\ y = Cx
Therefore, answer is (C)

Posted by

Gautam harsolia

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