Solve-dt-dx-2-x-t-

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

Solve :

\frac{dt}{d x} = \frac{2}{x + t} .

Answered by MrW3 last updated on 20/Aug/18

u = x + t

\frac{d u}{d x} = 1 + \frac{d t}{d x}

\Rightarrow \frac{d u}{d t} - 1 = \frac{2}{u}

\Rightarrow \frac{d u}{d t} = \frac{2 + u}{u}

\Rightarrow \frac{u d u}{2 + u} = d t

\Rightarrow (1 - \frac{2}{2 + u}) d u = d t

\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 ��