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  • Need clarity, kindly explain! - Differential equations - JEE Main-2

Solution of diffrential equaltion \frac{dy}{dx}= \frac{y+\sqrt{xy}}{x}   will be  

  • Option 1)

    2\sqrt{y/x}+ ln |x| = C

  • Option 2)

    2\sqrt{y/x}- ln |x| = C

  • Option 3)

    \sqrt{y/x}- ln |x| = C

  • Option 4)

    \sqrt{y/x}+ ln |x| = C

 

Answers (1)

best_answer

As we have learned

Homogeneous Differential Equation -

Put

\frac{y}{x}=v

\frac{dy}{dx}=v+\frac{xdv}{dx}

-

 

 Let y = vx \Rightarrow dy/dx = v + x dv/dv

v + x dv/dv = \frac{vx+\sqrt v x}{x} = v + \sqrt v

\Rightarrow xdv\dx = \sqrt v \Rightarrow dx/ \sqrt v- dx/x = 0

\int dx/ \sqrt v-\int dx/x= c \Rightarrow 2\sqrt v- ln |x|= c

2 \sqrt{y/x} - ln |x|= C

 


Option 1)

2\sqrt{y/x}+ ln |x| = C

Option 2)

2\sqrt{y/x}- ln |x| = C

Option 3)

\sqrt{y/x}- ln |x| = C

Option 4)

\sqrt{y/x}+ ln |x| = C

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