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  • Which of the following CANNOT be solved using variable separation method?Option: 1 <img alt="\frac{dy}{dx}=x+xy" src="https://learn.careers360.c

Which of the following CANNOT be solved using variable separation method?

Option: 1

\frac{dy}{dx}=x+xy


Option: 2

\frac{dy}{dx}=\sin x +y\sin x


Option: 3

\frac{dy}{dx}=x+\sin(x+y)


Option: 4

\frac{dy}{dx}=\frac{\left (1+x \right )}{(x+xy)}


Answers (1)

best_answer

For\; \; (A)\rightarrow \frac{dy}{dx}= x+xy\Rightarrow \frac{dy}{dx}= x(1+y)

\Rightarrow \frac{dy}{1+y}= xdx

For\: \: \left ( B \right )\rightarrow \frac{dy}{dx}= sinx+ysinx

\Rightarrow \frac{dy}{dx}= sinx(1+y)\Rightarrow \frac{dy}{1+y}= \sin xdx

For\: \: \left ( C \right )\rightarrow \frac{dy}{dx}= x+sin(x+y)

Here x and y can't be separated completely.

For\: \: \left ( D \right )\rightarrow \frac{dy}{dx}= \frac{1+x}{x+xy}

\Rightarrow \frac{dy}{dx}= \frac{1+x}{x(1+y)}

\Rightarrow(1+y) {dy}= \left ( \frac{1+x}{x} \right )dx

\therefore  (A), (B), and (D) are variable saperable but (C) is not

Posted by

Rakesh

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