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  • Tell me? Which of the following equation are reducible to homogenous form?

Which of the following equation are reducible to homogenous form? 

  • Option 1)

    \frac{dy}{dx}=\frac{2x+5y+1}{x^{2}+y}

  • Option 2)

    \frac{dy}{dx}=\frac{x-5y}{2x+3y+1}

  • Option 3)

    \frac{dy}{dx}=\frac{x+y^{2}}{x^{2}+y+1}

  • Option 4)

    \frac{dy}{dx}=\frac{x^{2}+y^{2}}{x+y+1}

 

Answers (1)

best_answer

As we have learned

Equations Reducible to the homogeneous form -

\frac{dy}{dx}=\frac{dY}{dx}\times\frac{dx}{dX} =\frac{dY}{dX}

- wherein

x= X+h

y= Y+k

 

 Equation of form \frac{dy}{dx}= \frac{ax+by+C}{Ax+By+C}  can be converted to homogeneous form

 


Option 1)

\frac{dy}{dx}=\frac{2x+5y+1}{x^{2}+y}

Option 2)

\frac{dy}{dx}=\frac{x-5y}{2x+3y+1}

Option 3)

\frac{dy}{dx}=\frac{x+y^{2}}{x^{2}+y+1}

Option 4)

\frac{dy}{dx}=\frac{x^{2}+y^{2}}{x+y+1}

Posted by

gaurav

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