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General and particular solutions

Describing equations

Concept 2 of 7 in Differential Equations

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Think about this

Both y=x2+1y = x^2 + 1 and y=x2−7y = x^2 - 7 satisfy dydx=2x\dfrac{dy}{dx} = 2x. How many solutions does this equation have, and which one passes through (1,5)(1, 5)?