CPM Homework Help : APCALC Problem 12-97

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

Step 1:

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

Step 2:

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

Step 3:

After integrating both sides:

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

Step 4:

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