Let $$ y^{\prime}=3 x $$. Find all values of $$ r $$ such that $$ y=r x^{2} $$ satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list. $$ r= $$

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1. Given $$ y = r x^2 $$, differentiate with respect to $$ x $$ to get
   $$
   y' = 2r x.
   $$

2. The differential equation is
   $$
   y' = 3x.
   $$

3. Equate the two expressions for $$ y' $$:
   $$
   2r x = 3x.
   $$

4. For $$ x \neq 0 $$, divide both sides by $$ x $$:
   $$
   2r = 3.
   $$

5. Solve for $$ r $$:
   $$
   r = \frac{3}{2}.
   $$

The only value of $$ r $$ that satisfies the differential equation is $$ \frac{3}{2} $$.
$$ r = \frac{3}{2} $$

Let .
Find all values of such that satisfies the differential equation. If
there is more than one correct answer, enter your answers as a comma
separated list.

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Let . Find all values of such that satisfies the differential equation. If there is more than one correct answer, enter your answers as a comma separated list.