The solution of dydx=(x-y)^2, y(1)=1, is:

Question

The solution of $\dfrac{dy}{dx}=(x-y)^2$, $y(1)=1$, is:

Accepted Answer

With $t=x-y$: $1-\dfrac{dt}{dx}=t^2 \implies \dfrac{dt}{1-t^2}=dx$; integrating gives $-x=\dfrac12\ln\left|\dfrac{t-1}{t+1}\right|+c$.

Using $(1,1)$: $c=-1$. Rearranged, this matches option B.

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