Review 6: Now You Try I

Identify which of the following are differential equations.

1. $y^{'} (t) = 2 t^{2} + 5 y$ $y'(t) = 2t^2+5y$

2. $y^{2} = 2 x y + x^{3}$ $y^2 = 2xy+ x^3$

3. $2 x P = \frac{d P}{d x} \cos (x) + P$ $2xP = \dfrac{dP}{dx} \cos(x) + P$

Solution:

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1. Yes, since it involves

y^{'} (t) .

$y'(t).$
2. No
3. Yes, since it involves

\frac{d P}{d x} .

$\dfrac{dP}{dx}.$