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Question Number 42221 by rahul 19 last updated on 20/Aug/18

$$\mathrm{Solve}:$$$$\frac{\mathrm{dt}}{\mathrm{d}x}=\frac{2}{x+\mathrm{t}}.$$

Answered by MrW3 last updated on 20/Aug/18

$$u=x+t$$$$\frac{du}{dx}=1+\frac{dt}{dx}$$$$\Rightarrow \frac{du}{dt}-1=\frac{2}{u}$$$$\Rightarrow \frac{du}{dt}=\frac{2+u}{u}$$$$\Rightarrow \frac{udu}{2+u}=dt$$$$\Rightarrow (1-\frac{2}{2+u})du=dt$$$$\Rightarrow u-2\ln (2+u)=t+C$$$$\Rightarrow (x+t)-2\ln (2+x+t)=t+C$$$$\Rightarrow x=2\ln (2+x+t)+C$$

Commented by rahul 19 last updated on 20/Aug/18

thanks sir ��

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