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The solution of the differential equation $d y = \tan^{2} (x + y) d x$

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sin2x+2y=2x−2y+c

cos2x+2y=2x−2y+c

cos2x−2y=2x+2y+c

sin2x−2y=2x+2y+c

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detailed solution

Correct option is A

dydx=tan2⁡(x+y) Put x+y=t⇒1+dydx=dtdxdtdx−1=tan2⁡t⇒dtdx=1+tan2⁡t=sec2⁡t⇒cos2⁡tdt=dx⇒∫1+cos⁡2t2dt=∫dx⇒12t+sin⁡2t2=x+c⇒14[2(x+y)+sin⁡2(x+y)]=x+c⇒sin⁡(2x+2y)=2x−2y+c

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The solution of the differential equation dy=tan2x+ydx

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The solution of the differential equation $d y = \tan^{2} (x + y) d x$