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(Solved): 1. Show that (x)=exx is an explicit solution to the diferential equation dxdy=e2xy2+(1 ...

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1. Show that

ϕ (x) = e^{x} - x

is an explicit solution to the diferential equation

\frac{d y}{d x} = e^{2 x} - y^{2} + (1 - 2 x) e^{x} + x^{2} - 1;

on the interval

(- \infty, \infty)

.

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