Exercise 1a

Determine the order of each differential equation, and whether or not the given functions are solutions of that equation. a) ( y ) 2 = 4 y ; y 1 ( x ) = x 2 , y 2 ( x ) = 2 x 2 , y 3 ( x ) = e x

Answers

( y ) 2 = 4 y is a first order ODE.
Let y ( x ) = y 1 ( x ) = x 2 and y 1 ( x ) = 2 x . Then,
( y ) 2 = 4 y ( 2 x ) 2 = 4 ( x 2 ) 4 x 2 = 4 x 2 .
Therefore, y 1 ( x ) = x 2 is a solution to this ODE.

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2025-07-17 18:19
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