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12-72.

What is the solution to the differential equation $y^2 · y^\prime − \operatorname{cos} x = 0$ with initial condition $y(0) = 3$ ?

$y = (3\operatorname{sin} x − \operatorname{sin} 3)^{\frac{1}{3}}$

$y = (3 \operatorname{sin} x)^{\frac{1}{3}}$

$y = \sqrt { \operatorname { sin } x }$

$y = (3\operatorname{sin} x + 27)^{\frac{1}{3}}$

$y = (3\operatorname{sin} x + 9)^{\frac{1}{3}}$

Steps:

After integrating both sides:
Use $(0, 3)$ to solve for the value of $C$ . Then write the equation in $y =$ form.

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