Exercise 1a

Question

Determine the order of each differential equation, and whether or not the given functions are solutions of that equation.
a) $(y')^{2}=4y; y_1(x) = x^2, y_2(x) = 2x^2, y_3(x) = e^{-x}$

Samuel Bertelson · Accepted Answer

$ (y')^{2} = 4y$ is a first order ODE.\
Let $y(x) = y_1(x) = x^{2}$ and $y'_1(x) = 2x$. Then,\
$ (y')^{2} = 4y \iff (2x)^{2} = 4(x^{2}) \iff 4x^{2} = 4x^{2}$.\
Therefore, $y_1(x) = x^{2}$ is a solution to this ODE.

Exercise 1a

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Exercise 1a

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