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# Show that the equation of the curve whose slope at any point is equal to $y+2x$ and which passes through the origin is $y\;=\;2(e^{x}-x-1)$

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Toolbox:
• Linear Differential equation.
• This is of the form $\large\frac{dy}{dx}$$+Py=Q where P and Q are functions of x only. • The integrating factor I= e^{\int \large pfd} and the G.S is ye^{\large pdx}=\int Q e^{\large pdx} dx+c Step 1: Given the slope is y+2x ie \large\frac{dy}{dx}$$=y+2x$

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