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  • Help me understand! Which of the following can be solved using variable separation method?

Which of the following can be solved using variable separation method?

  • Option 1)

    \frac{dy}{dx}= 1+xy

  • Option 2)

    \frac{dy}{dx}=x^{2}y

  • Option 3)

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

  • Option 4)

    \frac{dy}{dx}=x^{y}

 

Answers (1)

best_answer

As we learnt

 

Variable Separation Method -

If the coefficient of dx is only a function of x and that of dy is only function of y in the given differential equation

-

 

 

 

In (A),(C),and (D) x and y csnt be completely separated so as to make quantity involving x with dx and quantity involving y with dy But it can be done in (B) as 

\frac{dy}{dx}= x^{2}y\Rightarrow \frac{dy}{y}= x^{2}dx


Option 1)

\frac{dy}{dx}= 1+xy

Option 2)

\frac{dy}{dx}=x^{2}y

Option 3)

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

Option 4)

\frac{dy}{dx}=x^{y}

Posted by

Himanshu

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