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  • How to solve this problem- - Differential equations - JEE Main-5

Solution of diffrential equation x dy/dx+ y= xy \cos x  is 

  • Option 1)

    ln (xy)+ \cos x = C

  • Option 2)

    ln (xy)+ \sin x = C

  • Option 3)

    ln (xy)- \cos x = C

  • Option 4)

    ln (xy)= \sin x+ C

 

Answers (1)

best_answer

As we have learned

General form of Variable Separation -

d\left ( log xy \right )=\frac{ydx+xdy}{xy}

-

 

 Given equation can be written as xdy + y dx = xy cosx 

on dividing both sides by xy , we get 

\frac{xdy+ydx}{xy}= \cos xdx

\Rightarrow d(ln xy )= \cos xdx

 on integrating , it gives 

ln (xy ) = \ sin x + C

 


Option 1)

ln (xy)+ \cos x = C

Option 2)

ln (xy)+ \sin x = C

Option 3)

ln (xy)- \cos x = C

Option 4)

ln (xy)= \sin x+ C

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gaurav

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