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Question Number 170311 by Mastermind last updated on 20/May/22

$$5\frac{dy}{dx}=tan(2x+2y+6)$$$$$$$$Mastermind$$

Answered by mr W last updated on 20/May/22

$$t=2x+2y+6$$$$\frac{dt}{dx}=2+2\frac{dy}{dx}$$$$5(\frac{dt}{dx}-2)=2\tan t$$$$5\frac{dt}{dx}=2(\tan t+5)$$$$\frac{dt}{\tan t+5}=\frac{2dx}{5}$$$$\int \frac{dt}{\tan t+5}=\int \frac{2dx}{5}$$$$...$$$$\frac{5t+\ln (\sin t+5\cos t)}{26}=\frac{2x}{5}+C$$$$\frac{10(x+y+3)+\ln [\sin (2x+2y+6)+5\cos (2x+2y+6)]}{26}=\frac{2x}{5}+C$$

Commented by Mastermind last updated on 20/May/22

$$Sir,Isthatfinalanwer?$$$$andbesideswhichmethodisthis?$$

Commented by Mastermind last updated on 20/May/22

$$Thanks$$

Commented by Mastermind last updated on 20/May/22

$$Ireallyappreciate!$$

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