### Home > APCALC > Chapter 12 > Lesson 12.3.1 > Problem12-97

12-97.

Multiple Choice: What is the solution to the differential equation $y^2 · y′ - \cos(x) = 0$ with initial condition $y(0) = 3$?

1. $y = (3\sin(x) - \sin(3))^{1/3}$

1. $y = (3\sin(x))^{1/3}$

1. $y = \sqrt { \operatorname { sin } ( x ) }$

1. $y = (3\sin(x) + 27)^{1/3}$

1. $y = (3\sin(x) + 9)^{1/3}$

$y^2\frac{dy}{dx}-\cos(x)=0$

$y^2dy=\cos(x)dx$

After integrating both sides:

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

Use $\left(0, 3\right)$ to solve for the value of $C$. Then write the equation in $y =$ form.