Q. 213.5( 8 Votes )

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Answer :

Given that


This differential equation is of the form y’ + P(x)y = Q(x).


To solve such equation, we multiply the entire equation with integration factor .


Here


Then integration factor will be .


Let 1+x2=t


2x dx=dt.






Multiplying (1) with , we get





Integrating both sides








=tan-1 x + x + c


y = (1+x2)(tan-1 x + x + c)


OR


Given that



Integrating both sides




Let 2-ey=t


eydy=-dt



or



Hence ,
where



Or



Since bases of both logs are same, therefore the argument must be equal too



Simplifying this equation, we get



Since when x=0, y=0, therefore



or k=1


Hence,


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