Solve the following differential equation :  \frac{dx}{dy}+x= \left ( \tan y+\sec ^{2}y \right )
 

 

 

 

 
 
 
 
 

Answers (1)

The given D.E is of the form \frac{dx}{dy}+p\left ( y \right )x= Q\left ( y \right )
where p\left ( y \right )= 1\; \S \; Q\left ( y \right )= \tan y+\sec ^{2}y
Now IF =e^ {\int 1dy}= e^{y}
The solution is given as xe^{y}= \int \left ( \tan y+\sec ^{2}y \right )dy
ie              xe^{y}= e^{y}\left ( \tan y \right )+c\; or\; x= \tan y+e^{-y}c.

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