The solution of differential equation $ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y} f^{\prime}(\mathrm{x})-\mathrm{y}^{2}}{f(\mathrm{x})} $ is

Question

The solution of differential equation $ \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y} f^{\prime}(\mathrm{x})-\mathrm{y}^{2}}{f(\mathrm{x})} $ is, $ f(x)=y(x-c) $, $ f(x)=y(c-x) $, $ f(x)=y(x+c) $, None of these

MARKS App · Accepted Answer

The given equation is d y d x = y ƒ ′ x - y 2 ƒ x ⇒ y ƒ ′ x d x – ƒ x d y = y 2 d x ⇒ y ƒ ′ x d x - ƒ x d y y 2 = d x ⇒ d ƒ x y = d x On integration, we get ƒ x y = x + c ⇒ ƒ x = y x + c

Search any question & find its solution

Looking for more such questions to practice?